To measure the onset of mass transfer in eccentric binaries, we have developed a two‐phase smoothed particle hydrodynamics (SPH) technique. Mass transfer is important in the evolution of close binaries, and a key issue is to determine the separation at which mass transfer begins. The circular case is well understood and can be treated through the use of the Roche formalism. To treat the eccentric case, we use a newly developed two‐phase system. The body of the donor star is made up from high‐mass water particles, whilst the atmosphere is modelled with low‐mass oil particles. Both sets of particles take part fully in SPH interactions. To test the technique, we model circular mass‐transfer binaries containing a 0.6 M⊙ donor star and a 1 M⊙ white dwarf; such binaries are thought to form cataclysmic variable (CV) systems. We find that we can reproduce a reasonable CV mass‐transfer rate, and that our extended atmosphere gives a separation that is too large by approximately 16 per cent, although its pressure scale height is considerably exaggerated. We use the technique to measure the semimajor axis required for the onset of mass transfer in binaries with a mass ratio of q= 0.6 and a range of eccentricities. Comparing to the value obtained by considering the instantaneous Roche lobe at pericentre, we find that the radius of the star required for mass transfer to begin decreases systematically with increasing eccentricity.

The expected distributions of eclipse-depth versus period for eclipsing binaries of different luminosities are derived from large-scale population synthesis experiments. Using the rapid Hurley et al. BSE binary evolution code, we have evolved several hundred million binaries, starting from various simple input distributions of masses and orbit-sizes. Eclipse probabilities and predicted distributions over period and eclipsedepth (P/∆m) are given in a number of main-sequence intervals, from O-stars to brown dwarfs. The comparison between theory and Hipparcos observations shows that a standard (Duquennoy & Mayor) input distribution of orbit-sizes (a) gives reasonable numbers and P/∆m-distributions, as long as the mass-ratio distribution is also close to the observed flat ones. A random pairing model, where the primary and secondary are drawn independently from the same IMF, gives more than an order of magnitude too few eclipsing binaries on the upper main sequence. For a set of eclipsing OB-systems in the LMC, the observed period-distribution is different from the theoretical one, and the input orbit distributions and/or the evolutionary environment in LMC has to be different compared with the Galaxy. A natural application of these methods are estimates of the numbers and properties of eclipsing binaries observed by large-scale surveys like Gaia.

In hadronic collisions, the mini-jet cross section is formally divergent in the limit p ⊥ → 0. We argue that this divergence is tamed by some effective colour correlation length scale of the hadron. A toy model of the hadronic structure is introduced, that allows an estimate of the screening effects, and especially their energy dependence.

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