Properties of galaxy halos in Clusters and Voids
  We use the results of a high resolution N-body simulation to investigate the role of the environment on the formation and evolution of galaxy-sized halos. Starting from a set of constrained initial conditions, we have produced a final configuration hosting a double cluster in one octant and a large void extending over two octants of the simulation box. We present results for two statistics: the relationship between 1-D velocity dispersion and mass and the probability distribution of the spin parameter $P(\lambda)$. The \svm relationship is well reproduced by the Truncated Isothermal Sphere (TIS) model introduced by Shapiro et al. (1999), although the slope is different from the original prediction. A series of \svm relationships for different values of the anisotropy parameter $\beta$, obtained using the theoretical predictions by Lokas and Mamon (2001) for NFW density profiles are found to be only marginally consistent with the data. Using some properties of the equilibrium TIS models, we construct subsamples of {\em fiducial} equilibrium TIS halos from each of the three subregions, and we study their properties. For these halos, we do find an environmental dependence of their properties, in particular of the spin parameter distribution $P(\lambda)$. We study in more detail the TIS model, and we find new relationships between the truncation radius and other structural parameters. No gravitationally bound halo is found having a radius larger than the critical value for gravithermal instability for TIS halos (\rt $\ge 34.2 r_{0}$, where $r_{0}$ is the core radius of the TIS solution). We do however find a dependence of this relationship on the environment, like for the $P(\lambda)$ statistics. These facts hint at a possible r\^{o}le of tidal fields at determining the statistical properties of halos. 
V. Antonuccio-Delogu (Catania), U. Becciani (Catania), E. van Kampen   (Edinburgh), A. Pagliaro (Utrecht), A.B. Romeo (Onsal...