Exact Haldane mapping for all SS and super universality in spin chains

The low energy dynamics of the anti-ferromagnetic Heisenberg spin $S$ chain in the semiclassical limit $S\to\infty$ is known to map onto the O(3) nonlinear $\sigma$ model with a $\theta$ term in 1+1 dimension. Guided by the underlying dual symmetry of the spin chain, as well as the recently established topological significance of "dangling edge spins," we report an {\em exact} mapping onto the O(3) model that avoids the conventional large $S$ approximation altogether. Our new methodology demonstrates all the super universal features of the $\theta$ angle concept that previously arose in the theory of the quantum Hall effect. It explains why Haldane's original ideas remarkably yield the correct answer in spite of the fundamental complications that generally exist in the idea of semiclassical expansions

The Hydrodynamical Limit of Quantum Hall system

We study the current algebra of FQHE systems in the hydrodynamical limit of small amplitude, long-wavelength fluctuations. We show that the algebra simplifies considerably in this limit. The hamiltonian is expressed in a current-current form and the operators creating inter-Landau level and lowest Landau level collective excitations are identified.Comment: Revtex, 16 page

Selection bias in dynamically-measured super-massive black hole samples: consequences for pulsar timing arrays

Supermassive black hole -- host galaxy relations are key to the computation of the expected gravitational wave background (GWB) in the pulsar timing array (PTA) frequency band. It has been recently pointed out that standard relations adopted in GWB computations are in fact biased-high. We show that when this selection bias is taken into account, the expected GWB in the PTA band is a factor of about three smaller than previously estimated. Compared to other scaling relations recently published in the literature, the median amplitude of the signal at $f=1$yr$^{-1}$ drops from $1.3\times10^{-15}$ to $4\times10^{-16}$. Although this solves any potential tension between theoretical predictions and recent PTA limits without invoking other dynamical effects (such as stalling, eccentricity or strong coupling with the galactic environment), it also makes the GWB detection more challenging.Comment: 6 pages 4 figures, submitted to MNRAS letter

Acoustic radiation from lifting airfoils in compressible subsonic flow

The far field acoustic radiation from a lifting airfoil in a three-dimensional gust is studied. The acoustic pressure is calculated using the Kirchhoff method, instead of using the classical acoustic analogy approach due to Lighthill. The pressure on the Kirchhoff surface is calculated using an existing numerical solution of the unsteady flow field. The far field acoustic pressure is calculated in terms of these values using Kirchhoff's formula. The method is validated against existing semi-analytical results for a flat plate. The method is then used to study the problem of an airfoil in a harmonic three-dimensional gust, for a wide range of Mach numbers. The effect of variation of the airfoil thickness and angle of attack on the acoustic far field is studied. The changes in the mechanism of sound generation and propagation due to the presence of steady loading and nonuniform mean flow are also studied

Rotating fermions in two dimensions: Thomas Fermi approach

Properties of confined mesoscopic systems have been extensively studied numerically over recent years. We discuss an analytical approach to the study of finite rotating fermionic systems in two dimension. We first construct the energy functional for a finite fermionic system within the Thomas-Fermi approximation in two dimensions. We show that for specific interactions the problem may be exactly solved. We derive analytical expressions for the density, the critical size as well as the ground state energy of such systems in a given angular momentum sector.Comment: Latex 15 pages, 3 ps. figures. Poster in SCES-Y2K, held at SAHA Institute of Nuclear Physics,Calcutta,October (2000

ANTI-DIABETIC ACTIVITY OF HYDROALCOHOLIC EXTRACT OF EUGENIA JAMBOLANA LEAVES IN ALLOXAN INDUCED DIABETIC RATS

Objective: The present study was carried out to evaluate the antidiabetic activity of hydroalcoholic extracts of Eugenia jambolana leaves. Methods: The hydroalcoholic extracts of Eugenia jambolana by alloxan induced diabetic rats for 20 days. At high dose (400 mg/kg) it is exhibited significant anti- hyperglycaemic activity than hydroalcoholic extracts of Eugenia jambolana at low dose (200 mg/kg) in diabetic rats. Results: The hydroalcoholic extracts of Eugenia jambolana also showed improvement in parameters like body weight, Serum Cholesterol level and hepatic glycogen as well as regeneration of beta-cells of pancreas in diabetic rats. Conclusion: Histopathological studies reinforce the healing of kidney by hydroalcoholic extracts of Eugenia jambolana leaves as a possible mechanism of their antidiabetic activity. The present study provides a proof for the strong chemo taxonomical relationship for the plan

Majorana Spin Liquids on a two-leg ladder

We realize a gapless Majorana Orbital Liquid (MOL) using orbital degrees of freedom and also an SU(2)-invariant Majorana Spin Liquid (MSL) using both spin and orbital degrees of freedom in Kitaev-type models on a 2-leg ladder. The models are exactly solvable by Kitaev's parton approach, and we obtain long-wavelength descriptions for both Majorana liquids. The MOL has one gapless mode and power law correlations in energy at incommensuare wavevectors, while the SU(2) MSL has three gapless modes and power law correlations in spin, spin-nematic, and local energy observables. We study the stability of such states to perturbations away from the exactly solvable points. We find that both MOL and MSL can be stable against allowed short-range parton interactions. We also argue that both states persist upon allowing $Z_2$ gauge field fluctuations, in that the number of gapless modes is retained, although with an expanded set of contributions to observables compared to the free parton mean field.Comment: 15 pages, 6 figures. Revised versio