Analytic calculation of energies and wave functions of the quartic and pure quartic oscillators

Ground state energies and wave functions of quartic and pure quartic oscillators are calculated by first casting the Schr\"{o}dinger equation into a nonlinear Riccati form and then solving that nonlinear equation analytically in the first iteration of the quasilinearization method (QLM). In the QLM the nonlinear differential equation is solved by approximating the nonlinear terms by a sequence of linear expressions. The QLM is iterative but not perturbative and gives stable solutions to nonlinear problems without depending on the existence of a smallness parameter. Our explicit analytic results are then compared with exact numerical and also with WKB solutions and it is found that our ground state wave functions, using a range of small to large coupling constants, yield a precision of between 0.1 and 1 percent and are more accurate than WKB solutions by two to three orders of magnitude. In addition, our QLM wave functions are devoid of unphysical turning point singularities and thus allow one to make analytical estimates of how variation of the oscillator parameters affects physical systems that can be described by the quartic and pure quartic oscillators.Comment: 8 pages, 12 figures, 1 tabl

Effect of Long-lived Strongly Interacting Relic Particles on Big Bang Nucleosynthesis

It has been suggested that relic long-lived strongly interacting massive particles (SIMPs, or $X$ particles) existed in the early universe. We study effects of such long-lived unstable SIMPs on big bang nucleosynthesis (BBN) assuming that such particles existed during the BBN epoch, but then decayed long before they could be detected. The interaction strength between an $X$ particle and a nucleon is assumed to be similar to that between nucleons. We then calculate BBN in the presence of the unstable neutral charged $X^0$ particles taking into account the capture of $X^0$ particles by nuclei to form $X$-nuclei. We also study the nuclear reactions and beta decays of $X$-nuclei. We find that SIMPs form bound states with normal nuclei during a relatively early epoch of BBN. This leads to the production of heavy elements which remain attached to them. Constraints on the abundance of $X^0$ particles during BBN are derived from observationally inferred limits on the primordial light element abundances. Particle models which predict long-lived colored particles with lifetimes longer than $\sim$ 200 s are rejected based upon these constraints.Comment: 19 pages, 4 figure

Revised Relativistic Hydrodynamical Model for Neutron-Star Binaries

We report on numerical results from a revised hydrodynamic simulation of binary neutron-star orbits near merger. We find that the correction recently identified by Flanagan significantly reduces but does not eliminate the neutron-star compression effect. Although results of the revised simulations show that the compression is reduced for a given total orbital angular momentum, the inner most stable circular orbit moves to closer separation distances. At these closer orbits significant compression and even collapse is still possible prior to merger for a sufficiently soft EOS. The reduced compression in the corrected simulation is consistent with other recent studies of rigid irrotational binaries in quasiequilibrium in which the compression effect is observed to be small. Another significant effect of this correction is that the derived binary orbital frequencies are now in closer agreement with post-Newtonian expectations.Comment: Submitted to Phys. Rev.

The benefits of organic farming for biodiversity

Previous studies suggest widespread positive responses of biodiversity to organic farming. Many of these studies, however, have been small-scale. This project tested the generality of habitat and biodiversity differences between matched pairs of organic and non-organic farms containing cereal crops in lowland England on a large-scale across a range of taxa including plants, insects, birds and bats. The extent of both cropped and un-cropped habitats together with their composition and management on a range of scales were also compared. Organic farms was likely to favour higher levels of biodiversity and indeed organic farms tended to support higher numbers of species and overall abundance across most taxa. However, the magnitude of the response differed strikingly; plants showed stronger and more consistent responses than other taxa. Some, but not all, differences in biodiversity between systems appear to be a consequence of differences in habitat quantity

Multi-Instrument Observations of an MSTID over Arecibo Observatory

The Penn State All-Sky Imager (PSASI) at Arecibo Observatory provides planar horizontal context to the vertical ionospheric profiles obtained by the Incoherent Seatter Radar (TSR). Electric field measurements from the Communication/Navigation Outage Forecast System (C/NOFS) satellite are mapped down geomagnetic field lines to the height of the airglow layer; allowing multi-instrument studies of field-aligned irregularities with radar, imager, and satellite. A Medium-Scale Traveling Ionospheric Disturbance (MSTID) was observed during such a conjunction near the December solstice of 2009

Effects of structure formation on the expansion rate of the Universe: An estimate from numerical simulations

General relativistic corrections to the expansion rate of the Universe arise when the Einstein equations are averaged over a spatial volume in a locally inhomogeneous cosmology. It has been suggested that they may contribute to the observed cosmic acceleration. In this paper, we propose a new scheme that utilizes numerical simulations to make a realistic estimate of the magnitude of these corrections for general inhomogeneities in (3+1) spacetime. We then quantitatively calculate the volume averaged expansion rate using N-body large-scale structure simulations and compare it with the expansion rate in a standard FRW cosmology. We find that in the weak gravitational field limit, the converged corrections are slightly larger than the previous claimed 10^{-5} level, but not large enough nor even of the correct sign to drive the current cosmic acceleration. Nevertheless, the question of whether the cumulative effect can significantly change the expansion history of the Universe needs to be further investigated with strong-field relativity.Comment: 13 pages, 6 figures, improved version published in Phys. Rev.

Evolution systems for non-linear perturbations of background geometries

The formulation of the initial value problem for the Einstein equations is at the heart of obtaining interesting new solutions using numerical relativity and still very much under theoretical and applied scrutiny. We develop a specialised background geometry approach, for systems where there is non-trivial a priori knowledge about the spacetime under study. The background three-geometry and associated connection are used to express the ADM evolution equations in terms of physical non-linear deviations from that background. Expressing the equations in first order form leads naturally to a system closely linked to the Einstein-Christoffel system, introduced by Anderson and York, and sharing its hyperbolicity properties. We illustrate the drastic alteration of the source structure of the equations, and discuss why this is likely to be numerically advantageous.Comment: 12 pages, 3 figures, Revtex v3.0. Revised version to appear in Physical Review

Manipulating the Speed of Sound in a Two-Component Bose-Einstein Condensate

We consider a two-component weakly interacting Bose-Einstein condensate in the presence of an external field which couples the two components. We express the Hamiltonian in terms of the energy eigenstates of the single-body part of the Hamiltonian. These eigenstates are the atomic dressed states of quantum optics. When the energy difference between the two dressed states is much larger than the mean-field interactions, two-body interactions in the dressed state basis that do not conserve the number of atoms in each of the two dressed states are highly suppressed. The two-body interactions then take on a simplified form in the dressed basis with effective coupling constants that depend on the intensity and frequency of the external field. This implies that the chemical potential as well as the quasiparticle spectrum may be controlled experimentally in a simple manner. We demonstrate this by showing that one may achieve significant variations in the speed of sound in the condensate, a quantity which has been measured experimentally.Comment: 20 pages, 3 figures. Accepted for publication in Phys. Rev.

A non-linear Oscillator with quasi-Harmonic behaviour: two- and nn-dimensional Oscillators

A nonlinear two-dimensional system is studied by making use of both the Lagrangian and the Hamiltonian formalisms. The present model is obtained as a two-dimensional version of a one-dimensional oscillator previously studied at the classical and also at the quantum level. First, it is proved that it is a super-integrable system, and then the nonlinear equations are solved and the solutions are explicitly obtained. All the bounded motions are quasiperiodic oscillations and the unbounded (scattering) motions are represented by hyperbolic functions. In the second part the system is generalized to the case of $n$ degrees of freedom. Finally, the relation of this nonlinear system with the harmonic oscillator on spaces of constant curvature, two-dimensional sphere $S^2$ and hyperbolic plane $H^2$, is discussed.Comment: 30 pages, 4 figures, submitted to Nonlinearit

Binary Neutron-Star Systems: From the Newtonian Regime to the Last Stable Orbit

We report on the first calculations of fully relativistic binary circular orbits to span a range of separation distances from the innermost stable circular orbit (ISCO), deeply inside the strong field regime, to a distance ($\sim$ 200 km) where the system is accurately described by Newtonian dynamics. We consider a binary system composed of two identical corotating neutron stars, with 1.43 $M_\odot$ gravitational mass each in isolation. Using a conformally flat spatial metric we find solutions to the initial value equations that correspond to semi-stable circular orbits. At large distance, our numerical results agree exceedingly well with the Newtonian limit. We also present a self consistent determination of the ISCO for different stellar masses.Comment: 4 pages, 3 postscript figures. Data points added to fig 2; some issues clarified; references adde