On the Stability Domain of Systems of Three Arbitrary Charges

We present results on the stability of quantum systems consisting of a negative charge $-q_1$ with mass $m_{1}$ and two positive charges $q_2$ and $q_3$, with masses $m_{2}$ and $m_{3}$, respectively. We show that, for given masses $m_{i}$, each instability domain is convex in the plane of the variables $(q_{1}/q_{2}, q_{1}/q_{3})$. A new proof is given of the instability of muonic ions $(\alpha, p, \mu^-)$. We then study stability in some critical regimes where $q_3\ll q_2$: stability is sometimes restricted to large values of some mass ratios; the behaviour of the stability frontier is established to leading order in $q_3/q_2$. Finally we present some conjectures about the shape of the stability domain, both for given masses and varying charges, and for given charges and varying masses.Comment: Latex, 24 pages, 14 figures (some in latex, some in .eps

Classical SU(3) gauge field equations

Admissible forms of the static solutions to the SU(3) gauge field equation are examined. It is shown that by a proper choice of the form of solutions which extricate the SU(3) indices, the set of nonlinear partial differential equations is reducible to nonlinear ordinary differential equations for the radial functions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69698/2/JMAPAQ-15-1-53-1.pd

Fluid/gravity duality with Petrov-like boundary condition in a spacetime with a cosmological constant

Recently it has been shown that imposing Petrov type I condition on the boundary may reduce the Einstein's equation to the Navier-Stokes equation in the non-relativistic and near-horizon limit. In this paper we extend this framework to a spacetime with a cosmological constant. By explicit construction we show that the Navier-Stokes equation can be derived from both black brane background and spatially curved spacetime. We also conjecture that imposing Petrov type I condition on the boundary should be equivalent to the conventional method using the hydrodynamical expansion of the metric in the near horizon limit.Comment: 14 pages; Version published in PR

From Petrov-Einstein to Navier-Stokes in Spatially Curved Spacetime

We generalize the framework in arXiv:1104.5502 to the case that an embedding may have a nonvanishing intrinsic curvature. Directly employing the Brown-York stress tensor as the fundamental variables, we study the effect of finite perturbations of the extrinsic curvature while keeping the intrinsic metric fixed. We show that imposing a Petrov type I condition on the hypersurface geometry may reduce to the incompressible Navier-Stokes equation for a fluid moving in spatially curved spacetime in the near-horizon limit.Comment: 17 pages, references added, generalizing the metric form in part 3, version published in JHE

Stochastic Lorentz forces on a point charge moving near the conducting plate

The influence of quantized electromagnetic fields on a nonrelativistic charged particle moving near a conducting plate is studied. We give a field-theoretic derivation of the nonlinear, non-Markovian Langevin equation of the particle by the method of Feynman-Vernon influence functional. This stochastic approach incorporates not only the stochastic noise manifested from electromagnetic vacuum fluctuations, but also dissipation backreaction on a charge in the form of the retarded Lorentz forces. Since the imposition of the boundary is expected to anisotropically modify the effects of the fields on the evolution of the particle, we consider the motion of a charge undergoing small-amplitude oscillations in the direction either parallel or normal to the plane boundary. Under the dipole approximation for nonrelativistic motion, velocity fluctuations of the charge are found to grow linearly with time in the early stage of the evolution at the rather different rate, revealing strong anisotropic behavior. They are then asymptotically saturated as a result of the fluctuation-dissipation relation, and the same saturated value is found for the motion in both directions. The observational consequences are discussed. plane boundary. Velocity fluctuations of the charge are found to grow linearly with time in the early stage of the evolution at the rate given by the relaxation constant, which turns out to be smaller in the parallel case than in the perpendicular one in a similar configuration. Then, they are asymptotically saturated as a result of the fluctuation-dissipation relation. For the electron, the same saturated value is obtained for motion in both directions, and is mainly determined by its oscillatory motion. Possible observational consequences are discussed.Comment: 33 pages, 2 figure

Solar Mikheyev-Smirnov-Wolfenstein Effect with Three Generations of Neutrinos

Under the assumption that the density variation of the electrons can be approximated by an exponential function, the solar Mikheyev-Smirnov-Wolfenstein effect is treated for three generations of neutrinos. The generalized hypergeometric functions that result from the exact solution of this problem are studied in detail, and a method for their numerical evaluation is presented. This analysis plays a central role in the determination of neutrino masses, not only the differences of their squares, under the assumption of universal quark-lepton mixing.Comment: 22 pages, LaTeX, including 2 figure

The demand for sports and exercise: Results from an illustrative survey

Funding from the Department of Health policy research programme was used in this study.There is a paucity of empirical evidence on the extent to which price and perceived benefits affect the level of participation in sports and exercise. Using an illustrative sample of 60 adults at Brunel University, West London, we investigate the determinants of demand for sports and exercise. The data were collected through face-to-face interviews that covered indicators of sports and exercise behaviour; money/time price and perceived benefits of participation; and socio- economic/demographic details. Count, linear and probit regression models were fitted as appropriate. Seventy eight per cent of the sample participated in sports and exercise and spent an average of £27 per month and an average of 20 min travelling per occasion of sports and exercise. The demand for sport and exercise was negatively associated with time (travel or access time) and ‘variable’ price and positively correlated with ‘fixed’ price. Demand was price inelastic, except in the case of meeting the UK government’s recommended level of participation, which is time price elastic (elasticity = −2.2). The implications of data from a larger nationally representative sample as well as the role of economic incentives in influencing uptake of sports and exercise are discussed.This article is available through the Brunel Open Access Publishing Fund

Synthesis, Characterization, and Finite Size Effects on Electrical Transport of Nanoribbons of the Charge-Density Wave Conductor NbSe3

NbSe3 exhibits remarkable anisotropy in most of its physical properties and has been a model system for studies of quasi-one-dimensional charge-density-wave (CDW) phenomena. Herein, we report the synthesis, characterization, and electrical transport of single-crystalline NbSe3 nanoribbons by a facile one-step vapour transport process involving the transport of selenium powder onto a niobium foil substrate. Our investigations aid the understanding of the CDW nature of NbSe3 and the growth process of the material. They also indicate that NbSe3 nanoribbons have enhanced CDW properties compared to those of the bulk phase due to size confinement effects, thus expanding the search for new mesoscopic phenomena at the nanoscale level. Single nanoribbon measurements on the electrical resistance as a function of temperature show charge-density wave transitions at 59 K and 141 K. We also demonstrate significant enhancement in the depinning effect and sliding regimes mainly attributed to finite size effects.Comment: Version accepted for publicatio

Neutrino masses from universal Fermion mixing

If three right-handed neutrinos are added to the Standard Model, then, for the three known generations, there are six quarks and six leptons. It is then natural to assume that the symmetry considerations that have been applied to the quark matrices are also valid for the lepton mass matrices. Under this assumption, the solar and atmospheric neutrino data can be used to determine the individual neutrino masses. Using the \chi^2 fit, it is found that the mass of the lightest neutrino is (2-5)\times10^{-3} eV, that of the next heavier neutrino is (10-13)\times10^{-3} eV, while the mass of the heaviest neutrino is (52-54)\times10^{-3} eV.Comment: 27 pages, LaTeX, including several figure

Universality of low-energy scattering in (2+1) dimensions

We prove that, in (2+1) dimensions, the S-wave phase shift, $\delta_0(k)$, k being the c.m. momentum, vanishes as either $\delta_0 \to {c\over \ln (k/m)} or \delta_0 \to O(k^2)$ as $k\to 0$. The constant $c$ is universal and $c=\pi/2$. This result is established first in the framework of the Schr\"odinger equation for a large class of potentials, second for a massive field theory from proved analyticity and unitarity, and, finally, we look at perturbation theory in $\phi_3^4$ and study its relation to our non-perturbative result. The remarkable fact here is that in n-th order the perturbative amplitude diverges like $(\ln k)^n$ as $k\to 0$, while the full amplitude vanishes as $(\ln k)^{-1}$. We show how these two facts can be reconciled.Comment: 23 pages, Late