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Item Transfer of power in nonlinear gravitational clustering(Wiley-Blackwell, 1996-12-15) Bagla, J. S.; Padmanabhan, T.We investigate the transfer of power between different scales and the coupling of modes during the non-linear evolution of gravitational clustering in an expanding universe. We start with a power spectrum of density fluctuations that is exponentially damped outside a narrow range of scales, and use numerical simulations to study the evolution of this power spectrum. Non-linear effects generate power at other scales, with most power flowing from larger to smaller scales. The ‘cascade’ of power leads to equipartition of energy at smaller scales, implying a power spectrum with index n ~ - 1. We find that such a spectrum is produced in the range 1 < ð < 200 for density contrast ð. This result continues to hold even when small-scale power is added to the initial power spectrum. Semi-analytic models for gravitational clustering suggest a tendency for the effective index to move towards a critical index Nc ~-1. We find that such a spectrum is produced in the range 1< ð<200 for density contrast ð. This result continues to hold even when small-scale power is added to the initial power spectrum. Semi-analytic models for gravitational clustering suggest a tendency for the effective index to move towards a critical index Nc ~-1 in this range. For n< Nc , power in this range grows faster than linear rate, while if n> Nc , it grows at a slower rate- thereby changing the index closer to Nc. At scales larger than the narrow range of scales with initial power, a k⁴ tail is produced. We demonstrate that non-linear small scales do not affect the growth of perturbations at larger scales.Item New statistical indicator to study nonlinear gravitational clustering and structure formation(American Astronomical Society, 1996-04-22) Bagla, J. S.; Padmanabhan, T.In an = 1 universe dominated by nonrelativistic matter, velocity field and gravitational force field are proportional to each other in the linear regime. Neither of these quantities evolve in time and these can be scaled suitably so that the constant of proportionality is unity and velocity and force field are equal. The Zeldovich approximation extends this feature beyond the linear regime, until formation of pancakes. Nonlinear clustering which takes place after the breakdown of Zeldovich approximation, breaks this relation and the mismatch between these two vectors increases as the evolution proceeds. We suggest that the difference of these two vectors could form the basis for a powerful, new, statistical indicator of nonlinear clustering. We define an indicator called velocity contrast, study its behaviour using N-Body simulations and show that it can be used effectively to delineate the regions where nonlinear clustering has taken place.We discuss several features of this statistical indicator and provide simple analytic models to understand its behaviour. Particles with velocity contrast higher than a threshold have a correlation function which is biased with respect to the original sample. This bias factor is scale dependent and tends to unity at large scales.Item Neutral hydrogen at high redshifts as a probe of structure formation – III. Radio maps from N-body simulations.(Wiley-Blackwell, 1997-04-04) Bagla, J. S.; Nath, B. B.; Padmanabhan, T.Large inhomogeneities in neutral hydrogen in the universe can be detected at redshifts z 10 using the redshifted 21cm line emission. We use cosmological N-Body simulations for dark matter and a simple model for baryonic collapse to estimate the signal expected from structures like proto-clusters of galaxies at high redshifts.We study : (i) the standard CDM model, (ii) a modified CDM model with less power at small scales, and (iii) a +CDM model in a universe with 0 + = 1. We show that it should be possible for the next generation radio telescopes to detect such structures at the redshift 3.34 with an integration of about 100 hours. We also discuss possible schemes for enhancing signal to noise ratio to detect proto-condensates at high redshifts.