The mass and temperature functions in a moving barrier model
  In this paper, I use the extension of the excursion set model of Sheth & Tormen (2002) and the barrier shape obtained in Del Popolo & Gambera (1998) to calculate the unconditional halo mass function, and the conditional mass function in several cosmological models. I show that the barrier obtained in Del Popolo & Gambera (1998), which takes account of tidal interaction between proto-haloes, is a better description of the mass functions than the spherical collapse and is in good agreement with numerical simulations (Tozzi & Governato 1998, and Governato et al. 1999). The results are also in good agreement with those obtained by Sheth & Tormen (2002), only slight differences are observed expecially at the low mass end. I moreover calculate, and compare with simulations, the temperature function obtained by means of the mass functions previously calculated and also using an improved version of the M-T relation, which accounts for the fact that massive clusters accrete matter quasi-continuously, and finally taking account of the tidal interaction with neighboring clusters. Even in this case the discrepancy between the Press-Schecter predictions and simulations is considerably reduced. 
A. Del Popolo (1,2,3) ((1) Dipartimento di Matematica, Universit\`a   Statale di Bergamo, Bergamo, ITALY, (2) Feza Gursey In...