Research Publications
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Item Evolution of the Correlation Function for a Class of Processes involving Non Local Self - Replication(American Astronomical Society, 2002-11-01) Padmanabhan, T.Alarge class of evolutionary processes can be modeled by a rule that involves self-replication of some physical quantity with a nonlocal rescaling. We show that a class of such models is exactly solvable in the discrete as well as the continuum limit and can represent several physical situations, as varied as from the formation of galaxies in some cosmological models to growth of bacterial cultures. This class of models, in general, has no steady state solution and evolves unstably as as t → ∞ for generic initial conditions. The models can, however, exhibit an (unstable) power-law correlation function in the continuum limit, for an intermediate range of times and length scales.Item Gravitational collapse in an expanding universe: scaling relations for two-dimensional collapse revisited(Wiley-Blackwell, 2005-03-21) Ray, Suryadeep; Bagla, J. S.; Padmanabhan, T.We investigate non-linear scaling relations for two-dimensional (2D) gravitational collapse in an expanding background using a 2D TreePM code, and study the strongly non-linear regime ( ¯ξ 200) for power-law models. Evolution of these models is found to be scale invariant in all our simulations. We find that the stable clustering limit is not reached, but there is a model independent non-linear scaling relation in the asymptotic regime. This confirms results from an earlier study that only probed the mildly non-linear regime( ¯ξ 40). The correlation function in the extremely non-linear regime is a less steep function of scale than reported in earlier studies. We show that this is due to coherent transverse motions in massive haloes. We also study density profiles, and find that the scatter in the inner and outer slopes is large and that there is no single universal profile that fits all cases. We find that the difference in typical density profiles for different models is smaller than expected from similarity solutions for halo profiles, and transverse motions induced by substructure are a likely reason for this difference being small.