Hydraulic Jump in One-dimensional Flow

In the presence of viscosity the hydraulic jump in one dimension is seen to be a first-order transition. A scaling relation for the position of the jump has been determined by applying an averaging technique on the stationary hydrodynamic equations. This gives a linear height profile before the jump, as well as a clear dependence of the magnitude of the jump on the outer boundary condition. The importance of viscosity in the jump formation has been convincingly established, and its physical basis has been understood by a time-dependent analysis of the flow equations. In doing so, a very close correspondence has been revealed between a perturbation equation for the flow rate and the metric of an acoustic white hole. We finally provide experimental support for our heuristically developed theory.Comment: 17 Pages, 8 Figures, 1 Table. To appear in European Physical Journal

Ultracold bosons in a synthetic periodic magnetic field: Mott phases and re-entrant superfluid-insulator transitions

We study Mott phases and superfluid-insulator (SI) transitions of ultracold bosonic atoms in a two-dimensional square optical lattice at commensurate filling and in the presence of a synthetic periodic vector potential characterized by a strength $p$ and a period $l=qa$, where $q$ is an integer and $a$ is the lattice spacing. We show that the Schr\"odinger equation for the non-interacting bosons in the presence of such a periodic vector potential can be reduced to an one-dimensional Harper-like equation which yields $q$ energy bands. The lowest of these bands have either single or double minima whose position within the magnetic Brillouin zone can be tuned by varying $p$ for a given $q$. Using these energies and a strong-coupling expansion technique, we compute the phase diagram of these bosons in the presence of a deep optical lattice. We chart out the $p$ and $q$ dependence of the momentum distribution of the bosons in the Mott phases near the SI transitions and demonstrate that the bosons exhibit several re-entrant field-induced SI transitions for any fixed period $q$. We also predict that the superfluid density of the resultant superfluid state near such a SI transition has a periodicity $q$ ($q/2$) in real space for odd (even) $q$ and suggest experiments to test our theory.Comment: 8 pages, 11 figures, v

Anisotropic cosmological models with two fluids

In this paper, aniostropic dark energy cosmological models have been constructed in a Bianchi-V space-time with the energy momentum tensor consisting of two non-interacting fluids namely bulk viscous fluid and dark energy fluid. Two different models are constructed based on the power law cosmology and de Sitter universe. The constructed model also embedded with different pressure gradients along different spatial directions. The variable equation of state (EoS) parameter, skewness parameters for both the models are obtained and analyzed. The physical properties of the models obtained with the use of scale factors of power law and de Sitter law are also presented.Comment: 10 pages, 12 figure

Compact stars in f(R,T)f(R,T) gravity

In the present paper we generate a set of solutions describing the interior of a compact star under $f(R,T)$ theory of gravity which admits conformal motion. We consider the equation of state (EOS) $p=\omega\rho$ with $0<\omega<1$ for the fluid distribution consisting normal matter, $\omega$ being the EOS parameter. We therefore explore several aspects of the model analytically along with graphical representations to check the physical validity as well as acceptability of it within specified observational constraint in connection to a dozen of the compact star candidates. It is shown from the presented model that these objects are nothing but radiating compact stars.Comment: 16 pages, 6 figures, 1 table, substantial modification based on referee repor

Trends in social capital: Membership of associations in Great Britain, 1991–98

This Note uses the British Household Panel Study (BHPS) to consider the changing volume and distribution of voluntary association membership (and hence social capital) in Great Britain. We aim to supplement Hall's study of trends in social capital published in this Journal with more recent and longitudinal data. This allows us to show that whilst the volume of social capital is not declining, it is becoming increasingly class specific, and that its relative aggregate stability masks considerable turnover at the individual level. These findings are significant for current debates on social capital

Axially magnetized Dark Energy cosmological model

We investigate the behaviour of the skewness parameters for an anisotropic universe in the framework of General Relativity. Non interacting dark energy is considered in presence of electromagnetic field. A time varying deceleration parameter simulated by a hybrid scale factor is considered. The dynamics of the universe is investigated in presence and absence of magnetic field. The equation of state parameter of dark energy evolves within the range predicted by the observations. Magnetic field is observed to have a substantial effect on the cosmic dynamics and the skewness parameters. The models discussed here end in a big rip and become isotropic at finite time.Comment: 9 pages, 13 figures, Version accepted for publication in Mod. Phys. Lett.