Voronoi volume function:A new probe of cosmology and galaxy evolution

We study the Voronoi volume function (VVF) -- the distribution of cell volumes (or inverse local number density) in the Voronoi tessellation of any set of cosmological tracers (galaxies/haloes). We show that the shape of the VVF of biased tracers responds sensitively to physical properties such as halo mass, large-scale environment, substructure and redshift-space effects, making this a hitherto unexplored probe of both primordial cosmology and galaxy evolution. Using convenient summary statistics -- the width, median and a low percentile of the VVF as functions of average tracer number density -- we explore these effects for tracer populations in a suite of N-body simulations of a range of dark matter models. Our summary statistics sensitively probe primordial features such as small-scale oscillations in the initial matter power spectrum (as arise in models involving collisional effects in the dark sector), while being largely insensitive to a truncation of initial power (as in warm dark matter models). For vanilla cold dark matter (CDM) cosmologies, the summary statistics display strong evolution and redshift-space effects, and are also sensitive to cosmological parameter values for realistic tracer samples. Comparing the VVF of galaxies in the GAMA survey with that of abundance matched CDM (sub)haloes tentatively reveals environmental effects in GAMA beyond halo mass (modulo unmodelled satellite properties). Our exploratory analysis thus paves the way for using the VVF as a new probe of galaxy evolution physics as well as the nature of dark matter and dark energy.Comment: 20 pages, 15 figures; v2 - minor changes to match version accepted in MNRA

A detailed review of blockchain-based applications for protection against pandemic like COVID-19

The recent corona virus disease (COVID-19) pandemic has brought the issues of technological deficiencies and challenges of security and privacy, validating and maintaining anonymity, user control over records while fully utilizing the available records etc., that can be encountered in an emergency or pandemic condition. Blockchain technology has evolved as a promising solution in conditions that necessitate immutability, record integrity, and proper records authentication. Blockchain can effectively resolve the technical barriers and effectively utilize the available resources and infrastructure in pandemic situations like the current COVID-19. This paper provides an extensive review of various possible use cases of blockchain and available solutions for protection against the COVID-19 like situation. It gives an insight into the benefits and shortcomings of available solutions. It further provides the issues and challenges of adopting blockchain in a situation like COVID-19 and suggest future directions that can offer a platform for further improved and better solutions

Renormalization of shell model of turbulence

Renormalization enables a systematic scale-by-scale analysis of multiscale systems. In this paper, we employ \textit{renormalization group} (RG) to the shell model of turbulence and show that the RG equation is satisfied by $|u_n|^2 =K_\mathrm{Ko} \epsilon^{2/3} k_n^{-2/3}$ and $\nu_n = \nu_* \sqrt{K_\mathrm{Ko}} \epsilon^{1/3} k_n^{-4/3}$, where $k_n, u_n$ are the wavenumber and velocity of shell $n$; $\nu_*, K_\mathrm{Ko}$ are RG and Kolmogorov's constants; and $\epsilon$ is the energy dissipation rate. We find that $\nu_* \approx 0.5$ and $K_\mathrm{Ko} \approx 1.7$, consistent with earlier RG works on Navier-Stokes equation. We verify the theoretical predictions using numerical simulations.Comment: To appear in Phys. Rev.