| Summary: | A rapid binary evolution algorithm is produced that enables modelling of even the most complex binary systems. In addition to all aspects of the single star algorithm, features such as mass transfer, mass accretion, common-envelope evolution, collisions, supernova kicks and angular momentum loss mechanisms are included. Circularization and synchronization of the orbit owing to tidal interactions are calculated for convective, radiative and degenerate damping mechanisms. The algorithm is used to study the formation and evolution of various binary systems. The effect that tidal friction has on the outcome of binary evolution is investigated. The rapid binary code is used to generate a series of large binary populations enabling the formation rate of interesting individual species and events to be calculated. By comparing the results for populations with and without tidal friction it is possible to quantify the hitherto ignored systematic effects of tides and how that modelling of tidal evolution in binary systems is necessary in order to draw accurate conclusions from population synthesis work. The rapid single star and binary star evolution algorithms are incorporated into a state-of-the-art <I>N</I>-body. This code is used to explore the evolution of a primordial binary population as a function of radius in a globular cluster. HST images of the young rich LMC cluster NGC 1818 have revealed a binary fraction that increases towards the cluster centre, from ~ 20 ±5% in the outer parts, to ~ 35 ± 5% inside the core. A comparison with the results of the <I>N</I>-body models suggests that this is consistent with dynamical mass segregation and need not be primordial. In order to investigate the incidence and distribution of blue straggler starts in a cluster environment, <I>N</I>-body models are generated for comparison with observations of the old open cluster M67. The effectiveness of proposed blue straggler formation mechanisms, such as mass transfer within a binary system or the collision of two main sequence stars, is tested. The nature and extent of the binary population required to produce the observed numbers of blue stragglers is constrained. The escape of stars from the tidal radius of a cluster as it evolves is discussed and an estimate of the escape rate given.
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