| In this PhD thesis, we focus on cosmological simulations on small scale structure of nonlinear evolution. We study the density profile for the effect of a physical bias of mass resolution, and find a proper way that can affect the density profile.In the first chapter, we introduced the background of this problem and draw out the definition of it. Firstly, we introduced the observational background of dark matter, and the particle candidates of particle physics. Then we briefly the evolution history of N-body simulation: the exponential increasing particle number N; the great success on studies of large scale structure formation; but also some results not agree will with observations the "cusp problem" & the "substructure problem". Then we introduced some factors that can affect the simulation result: the particle number, the softening factor and the limited scale of time step. At last, we gave the definition of AE bias and the problem it bring us.In the second chapter, we mainly discuss the effect of the AE bias on micro-scale of the system. At the beginning, we introduced another style of systems buildup of particles of pure gravitational interaction-some virialized star clusters, such as the globular clusters, the ellipse galaxies and the galactic nuclei. Then we briefly give a review about the theoretic model about the macroscopical property of these system. Then we studied an important difference on microscopical of the dark matter halo in simulation and in nature: We have show that both the relaxation time and the mean free path is direct proportion of particle number. The AE bias can make both Ls and trelax greatly shorten and make the two-body relaxation can not be neglect. We estimate the equivalent scattering section, and find the σae come with the AE bias is just a little smaller than the σSI of the SIDM model. We designed two numerical simulation experiment to detect the effect of AE bias: our simulation results shows that the Ei and Li will soon be...
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