Ionization fronts and their interaction with density fluctuations:   implications for reionization
  The propagation of cosmological ionization fronts (I-fronts) during reionization is strongly influenced by small-scale structure. Here we summarize our recent attemps to understand the effect of this small-scale structure. We present high resolution cosmological N-body simulations at high-z (z>6) which resolve a wide range of halo mass, from minihalos to clusters of large, rare halos. We also study how minihalos affect I-fronts, through simulations of minihalo photoevaporation. Furthermore, we modify the I-front propagation equations to account for evolving small-scale structure, and incorporate these results into a semi-analytical reionization model. When intergalactic medium clumping and minihalo clustering around sources are included, small-scale structure affects reionization by slowing it down and extending it in time. This helps to explain observations by the Wilkinson Microwave Anisotropy Probe, which imply an early and extended reionization epoch. We also study how source clustering affects the evolution and size of H II regions, finding, in agreement with simulations, that H II regions usually expand, rarely shrinking. Hence, "relic H II regions'' are an exception, rather than the rule. When the suppression of small-mass sources in already-ionized regions by Jeans-mass filtering is accounted for, H II regions are smaller, delaying overlap. We also present a new numerical method for radiative transfer which is fast, efficient, and easily coupled to hydrodynamics and N-body codes, along with sample tests and applications. 
Ilian T. Iliev, Paul R. Shapiro, Evan Scannapieco, Garrelt Mellema,   Marcelo A. Alvarez, Alejandro C. Raga, and Ue-Li Pen