A Simple Method for Computing the Non-Linear Mass Correlation Function with Implications for Stable Clustering

We propose a simple and accurate method for computing analytically the mass correlation function for cold dark matter and scale-free models that fits N-body simulations over a range that extends from the linear to the strongly non-linear regime. The method, based on the dynamical evolution of the pair conservation equation, relies on a universal relation between the pair-wise velocity and the smoothed correlation function valid for high and low density models, as derived empirically from N-body simulations. An intriguing alternative relation, based on the stable-clustering hypothesis, predicts a power-law behavior of the mass correlation function that disagrees with N-body simulations but conforms well to the observed galaxy correlation function if negligible bias is assumed. The method is a useful tool for rapidly exploring a wide span of models and, at the same time, raises new questions about large scale structure formation.Comment: 10 pages, 3 figure

Band Structure of the Fractional Quantum Hall Effect

The eigenstates of interacting electrons in the fractional quantum Hall phase typically form fairly well defined bands in the energy space. We show that the composite fermion theory gives insight into the origin of these bands and provides an accurate and complete microscopic description of the strongly correlated many-body states in the low-energy bands. Thus, somewhat like in Landau's fermi liquid theory, there is a one-to-one correspondence between the low energy Hilbert space of strongly interacting electrons in the fractinal quantum Hall regime and that of weakly interacting electrons in the integer quantum Hall regime.Comment: 10 page

The relation between the two-point and the three-point correlation functions in the non-linear gravitational clustering regime

The connection between the two-point and the three-point correlation functions in the non-linear gravitational clustering regime is studied. Under a scaling hypothesis, we find that the three-point correlation function, $\zeta$, obeys the scaling law $\zeta\propto \xi^{\frac{3m+4w-2\epsilon}{2m+2w}}$ in the nonlinear regime, where $\xi$, $m$, $w$, and $\epsilon$ are the two-point correlation function, the power index of the power spectrum in the nonlinear regime, the number of spatial dimensions, and the power index of the phase correlations, respectively. The new formula reveals the origin of the power index of the three-point correlation function. We also obtain the theoretical condition for which the ``hierarchical form'' $\zeta\propto\xi^2$ is reproduced.Comment: 16 pages, 4 figures. Accepted for publication in APJ. Some sentences and figures are revise

Depression among Adolescent Students in a Rural Block of Haryana: A Cross Sectional Study

Background: Depression among adolescent is an area of increasing concern worldwide. This study aimed to assess the prevalence of depression among school going adolescents in government and private schools in a rural area of block Beri of Haryana. Methods: A cross sectional study was conducted in a sample size of 600 students (300 males and 300 females) studying in class 8th to 12th. A pre designed, pre tested tool SCL 90 R containing 90 items was used to screen depression in these students. Depression is one of the psychiatric morbidity screened by this tool. Cut off point of estimated raw score of 1 was used to label as depression. All the statistical analysis was carried out using SPSS 20. Results: The overall prevalence of depression was found to be 39.1% with mild depression to be 33.1% and moderate to severe depression to be 6%. Depression was significantly more among female students (45%) than male students (33.3%). Overall prevalence of depression significantly increased with age. It was found to be 34.3% among 13-14 years age-group, 41% among 15-16 years age-group and 57.1% among 17-19 years age-group. The association of depression with other socio demographic profile like socio economic status, literacy level of mother and father, employment status of mother was found to be non-significant. Conclusion: It is concluded from the present study that more than one – third (39%) of school adolescents suffered from depression. Reasons for such high prevalence of depression need to be determined. At the same time teachers and parents should be made aware of this problem and appropriate counselling of students should be done through regular school-based screening programme.

One-Dimensional Theory of the Quantum Hall System

We consider the lowest Landau level on a torus as a function of its circumference $L_1$. When $L_1\to 0$, the ground state at general rational filling fraction is a crystal with a gap--a Tao-Thouless state. For filling fractions $\nu=p/(2pm+1)$, these states are the limits of Laughlin's or Jain's wave functions describing the gapped quantum Hall states when $L_1\to \infty$. For the half-filled Landau level, there is a transition to a Fermi sea of non-interacting neutral dipoles, or rather to a Luttinger liquid modification thereof, at $L_1\sim5$ magnetic lengths. This state is a version of the Rezayi-Read state, and develops continuously into the state that is believed to describe the observed metallic phase as $L_1\to \infty$. Furthermore, the effective Landau level structure that emerges within the lowest Landau level follows from the magnetic symmetries.Comment: 4 pages, 1 figur

Dynamics of pairwise motions

We derive a simple closed-form expression, relating \vs(r) -- the mean relative velocity of pairs of galaxies at fixed separation $r$ -- to the two-point correlation function of mass density fluctuations, $\xi(r)$. We compare our analytic model for \vs(r) with N-body simulations, and find excellent agreement in the entire dynamical range probed by the simulations (0.1 \lsim \xi \lsim 1000). Our results can be used to estimate the cosmological density parameter, \Om, directly from redshift-distance surveys, like Mark III.Comment: 10 pages 2 Figs., submitted to ApJ Let

Projectile Δ\Delta Excitations in p(p,n)Nπp(p,n)N\pi Reactions

It has recently been proven from measurements of the spin-transfer coefficients $D_{xx}$ and $D_{zz}$ that there is a small but non-vanishing $\Delta S=0$ component $\sigma_{0}$, in the inclusive $p(p,n)N\pi\,$ reaction cross section $\sigma\,$. It is shown that the dominant part of the measured $\sigma_{0}$ can be explained in terms of the projectile $\Delta$ excitation mechanism. An estimate is further made of contributions to $\sigma_{0}$ from s-wave rescattering process. It is found that s-wave rescattering contribution is much smaller than the contribution coming from projectile $\Delta$ excitation mechanism. The addition of s-wave rescattering contribution to the dominant part, however, improves the fit to the data.Comment: 9 pages, Revtex, figures can be obtained upon reques