Reionization, SLOAN, and WMAP: is the Picture Consistent?

I show that advanced simulations of cosmological reionization are able to fit the observed data on the mean transmitted flux in the hydrogen Lyman-alpha line at z~6. At the same time, posteriori models can be constructed that also produce a large value (20%) for the Thompson scattering optical depth, consistent with the WMAP measurements. Thus, it appears that a consistent picture emerges in which early reionization (as suggested by WMAP) is complete by z~6 in accord with the SLOAN data.Comment: accepted for publication in Ap

Probing the universe with the Lyman-alpha forest: II. The column density distribution

I apply the well controlled Hydro-PM approximation of Gnedin & Hui to model the column density distribution of the Lyman-alpha forest for 25 different flat cosmological scenarios, including variants of the standard CDM, tilted CDM, CDM with a cosmological constant, and CHDM models. I show that within the accuracy of the HPM approximation the slope of the column density distribution reflects the degree of nonlinearity of the cosmic gas distribution and is a function of the rms linear density fluctuation at the characteristic filtering scale only. The amplitude of the column density distribution, expressed as the value for the ionizing intensity, is derived as a function of the cosmological parameters (to about 40% accuracy). The observational data are currently consistent with the value for the ionizing intensity being constant in the redshift interval z~2-4.Comment: Revised version; submitted to MNRA

Sub-diffusion in External Potential: Anomalous hiding behind Normal

We propose a model of sub-diffusion in which an external force is acting on a particle at all times not only at the moment of jump. The implication of this assumption is the dependence of the random trapping time on the force with the dramatic change of particles behavior compared to the standard continuous time random walk model. Constant force leads to the transition from non-ergodic sub-diffusion to seemingly ergodic diffusive behavior. However, we show it remains anomalous in a sense that the diffusion coefficient depends on the force and the anomalous exponent. For the quadratic potential we find that the anomalous exponent defines not only the speed of convergence but also the stationary distribution which is different from standard Boltzmann equilibrium.Comment: 6 pages, 3 figure

Emergence of L\'{e}vy Walks in Systems of Interacting Individuals

Recent experiments (G. Ariel, et al., Nature Comm. 6, 8396 (2015)) revealed an intriguing behavior of swarming bacteria: they fundamentally change their collective motion from simple diffusion into a superdiffusive L\'{e}vy walk dynamics. We introduce a nonlinear non-Markovian persistent random walk model that explains the emergence of superdiffusive L\'{e}vy walks. We show that the alignment interaction between individuals can lead to the superdiffusive growth of the mean squared displacement and the power law distribution of run length with infinite variance. The main result is that the superdiffusive behavior emerges as a nonlinear collective phenomenon, rather than due to the standard assumption of the power law distribution of run distances from the inception. At the same time, we find that the repulsion/collision effects lead to the density dependent exponential tempering of power law distributions. This qualitatively explains experimentally observed transition from superdiffusion to the diffusion of mussels as their density increases (M. de Jager et al., Proc. R. Soc. B 281, 20132605 (2014))