New views of the solar wind with the Lambert W function

This paper presents closed-form analytic solutions to two illustrative problems in solar physics that have been considered not solvable in this way previously. Both the outflow speed and the mass loss rate of the solar wind of plasma particles ejected by the Sun are derived analytically for certain illustrative approximations. The calculated radial dependence of the flow speed applies to both Parker's isothermal solar wind equation and Bondi's equation of spherical accretion. These problems involve the solution of transcendental equations containing products of variables and their logarithms. Such equations appear in many fields of physics and are solvable by use of the Lambert W function, which is briefly described. This paper is an example of how new functions can be applied to existing problems.Comment: 16 pages (revtex4), 3 figures, American J. Phys., in press (2004

The Carter Constant for Inclined Orbits About a Massive Kerr Black Hole: I. circular orbits

In an extreme binary black hole system, an orbit will increase its angle of inclination (i) as it evolves in Kerr spacetime. We focus our attention on the behaviour of the Carter constant (Q) for near-polar orbits; and develop an analysis that is independent of and complements radiation reaction models. For a Schwarzschild black hole, the polar orbits represent the abutment between the prograde and retrograde orbits at which Q is at its maximum value for given values of latus rectum (l) and eccentricity (e). The introduction of spin (S = |J|/M2) to the massive black hole causes this boundary, or abutment, to be moved towards greater orbital inclination; thus it no longer cleanly separates prograde and retrograde orbits. To characterise the abutment of a Kerr black hole (KBH), we first investigated the last stable orbit (LSO) of a test-particle about a KBH, and then extended this work to general orbits. To develop a better understanding of the evolution of Q we developed analytical formulae for Q in terms of l, e, and S to describe elliptical orbits at the abutment, polar orbits, and last stable orbits (LSO). By knowing the analytical form of dQ/dl at the abutment, we were able to test a 2PN flux equation for Q. We also used these formulae to numerically calculate the di/dl of hypothetical circular orbits that evolve along the abutment. From these values we have determined that di/dl = -(122.7S - 36S^3)l^-11/2 -(63/2 S + 35/4 S^3) l^-9/2 -15/2 S l^-7/2 -9/2 S l^-5/2. Thus the abutment becomes an important analytical and numerical laboratory for studying the evolution of Q and i in Kerr spacetime and for testing current and future radiation back-reaction models for near-polar retrograde orbits.Comment: 51 pages, 8 figures, accepted by Classical and Quantum Gravity on September 22nd, 201

The Study of the Heisenberg-Euler Lagrangian and Some of its Applications

The Heisenberg-Euler Lagrangian is not only a topic of fundamental interest, but also has a rich variety of diverse applications in astrophysics, nonlinear optics and elementary particle physics etc. We discuss the series representation of this Lagrangian and a few of its applications in this study. [In an appendix, we discuss issues related to the renormalization - and the renormalization-group invariance - of the Heisenberg-Euler Lagrangian and its two-loop generalization.]Comment: 12 pages, LaTeX; Proceedings of the MRST-2003 conference; talk given by S. R. Vallur

Global parameter-space correlations of coherent searches for continuous gravitational waves

The space of phase-parameters (sky-position, frequency, spindowns) of a coherent matched-filtering search for continuous gravitational waves from isolated neutron stars shows strong global correlations (``circles in the sky''). In the local limit this can be analysed in terms of a parameter-space metric, but the global properties are less well studied. In this work we report on our recent progress in understanding these global correlations analytically for short to intermediate (less than a month, say) observation times and neglecting spindowns. The location of these correlation-circles in parameter-space is found to be determined mostly by the orbital velocity of the earth, while the spin-motion of the detector and the antenna-patterns only contribute significantly to the amplitude of the detection statistic along these circles.Comment: 10 pages, 6 figures; contribution to GWDAW9, submitted to CQ

Materials research at National Aeronautical Laboratory (contributions of S Ramaseshan)

Materials research programmes of the National Aeronautical Laboratory and Prof. Ramaseshan's contributions to these are presented in this article

Lamm, Valluri, Jentschura and Weniger comment on "A Convergent Series for the QED Effective Action" by Cho and Pak [Phys. Rev. Lett. vol. 86, pp. 1947-1950 (2001)]

Complete results were obtained by us in [Can. J. Phys. 71, 389 (1993)] for convergent series representations of both the real and the imaginary part of the QED effective action; these derivations were based on correct intermediate steps. In this comment, we argue that the physical significance of the "logarithmic correction term" found by Cho and Pak in [Phys. Rev. Lett. 86, 1947 (2001)] in comparison to the usual expression for the QED effective action remains to be demonstrated. Further information on related subjects can be found in Appendix A of hep-ph/0308223 and in hep-th/0210240.Comment: 1 page, RevTeX; only "meta-data" update

The impact of baryons on the direct detection of dark matter

The spatial and velocity distributions of dark matter particles in the Milky Way Halo affect the signals expected to be observed in searches for dark matter. Results from direct detection experiments are often analyzed assuming a simple isothermal distribution of dark matter, the Standard Halo Model (SHM). Yet there has been skepticism regarding the validity of this simple model due to the complicated gravitational collapse and merger history of actual galaxies. In this paper we compare the SHM to the results of cosmological hydrodynamical simulations of galaxy formation to investigate whether or not the SHM is a good representation of the true WIMP distribution in the analysis of direct detection data. We examine two Milky Way-like galaxies from the MaGICC cosmological simulations (a) with dark matter only and (b) with baryonic physics included. The inclusion of baryons drives the shape of the DM halo to become more spherical and makes the velocity distribution of dark matter particles less anisotropic especially at large heliocentric velocities, thereby making the SHM a better fit. We also note that we do not find a significant disk-like rotating dark matter component in either of the two galaxy halos with baryons that we examine, suggesting that dark disks are not a generic prediction of cosmological hydrodynamical simulations. We conclude that in the Solar neighborhood, the SHM is in fact a good approximation to the true dark matter distribution in these cosmological simulations (with baryons) which are reasonable representations of the Milky Way, and hence can also be used for the purpose of dark matter direct detection calculations.Comment: Minor changes to match JCAP version. 21 pages, 9 figure

The Analysis of Large Order Bessel Functions in Gravitational Wave Signals from Pulsars

In this work, we present the analytic treatment of the large order Bessel functions that arise in the Fourier Transform (FT) of the Gravitational Wave (GW) signal from a pulsar. We outline several strategies which employ asymptotic expansions in evaluation of such Bessel functions which also happen to have large argument. Large order Bessel functions also arise in the Peters-Mathews model of binary inspiralling stars emitting GW and several problems in potential scattering theory. Other applications also arise in a variety of problems in Applied Mathematics as well as in the Natural Sciences and present a challenge for High Performance Computing(HPC).Comment: 8 pages, Uses IEEE style files: Ieee.cls, Ieee.clo and floatsty.sty. Accepted for publication in High Performance Computing Symposium, May 15-18 (HPCS 2005) Guelph, Ontario, Canad