PERCOLATION ANALYSIS OF NONLINEAR STRUCTURES IN SCALE-FREE 2-DIMENSIONAL SIMULATIONS

We present results of applying percolation analysis to several two-dimensional N-body models which simulate the formation of large-scale structure. Three parameters are estimated: total area (a(c)), total mass (M(c)), and percolation density (rho(c)) of the percolating structure at the percolation threshold for both unsmoothed and smoothed (with different scales L(s)) nonlinear density fields. We found that the power-law models with n = 0 in two dimensions show a clear signal associated with filamentary structures, confirming early speculations that this type of model has several features of filamentary-type distributions. Also, we have shown that by properly applying smoothing techniques, many problems previously considered detrimental can be dealt with and overcome. We discuss possible difficulties and prospects with the use of this method, specifically relating to techniques and methods already applied to CfA deep sky surveys. The success of this test in two dimensions and the potential for extrapolation to three dimensions is also discussed.