Surface r Modes and Burst Oscillations of Neutron Stars

We study the $r$-modes propagating in steadily mass accreting, nuclear burning, and geometrically thin envelopes on the surface of rotating neutron stars. For the modal analysis, we construct the envelope models which are fully radiaitive or have a convective region. As the angular rotation frequency $\Omega$ is increased, the oscillation frequency $\omega$ of the $r$-modes in the thin envelopes deviates appreciably from the asymptotic frequency $\omega=2m\Omega/l^\prime(l^\prime+1)$ defined in the limit of $\Omega\to 0$, where $\omega$ is the frequency observed in the corotating frame of the star, and $m$ and $l^\prime$ are the indices of the spherical harmonic function $Y_{l^\prime}^m$ representing the angular dependence of the modes. We find that the fundamental $r$-modes in the convective models are destabilized by strong nuclear burning in the convective region. Because of excessive heating by nuclear buring, the corotating-frame oscillation frequency $\omega$ of the $r$-modes in the convective models becomes larger, and hence the inertial-frame oscillation frequency $|\sigma|$ becomes smaller, than those of the corresopnding $r$-modes in the radiative models, where $\sigma=\omega-m\Omega$ is negative for the $r$-modes of positive $m$. We find that the relative frequency change $f=-(\sigma_{conv}-\sigma_{rad})/\sigma_{rad}$ is always positive and becomes less than $\sim$0.01 for the fundamental $r$-modes of $l^\prime>|m|+1$ at $|\sigma_{rad}|/2\pi\sim$300Hz for $m=1$ or at $|\sigma_{rad}|/2\pi\sim$600Hz for $m=2$, where $\sigma_{conv}$ and $\sigma_{rad}$ denote the oscillation frequencies for the convective and the radiative envelope models, respectively.Comment: 20 pages, 12 figure

L2L_2 boosting in kernel regression

In this paper, we investigate the theoretical and empirical properties of $L_2$ boosting with kernel regression estimates as weak learners. We show that each step of $L_2$ boosting reduces the bias of the estimate by two orders of magnitude, while it does not deteriorate the order of the variance. We illustrate the theoretical findings by some simulated examples. Also, we demonstrate that $L_2$ boosting is superior to the use of higher-order kernels, which is a well-known method of reducing the bias of the kernel estimate.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ160 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Generalised additive dependency inflated models including aggregated covariates

Let us assume that X, Y and U are observed and that the conditional mean of U given X and Y can be expressed via an additive dependency of X, λ(X)Y and X + Y for some unspecified function . This structured regression model can be transferred to a hazard model or a density model when applied on some appropriate grid, and has important forecasting applications via structured marker dependent hazards models or structured density models including age-period-cohort relationships. The structured regression model is also important when the severity of the dependent variable has a complicated dependency on waiting times X, Y and the total waiting time X+Y . In case the conditional mean of U approximates a density, the regression model can be used to analyse the age-period-cohort model, also when exposure data are not available. In case the conditional mean of U approximates a marker dependent hazard, the regression model introduces new relevant age-period-cohort time scale interdependencies in understanding longevity. A direct use of the regression relationship introduced in this paper is the estimation of the severity of outstanding liabilities in non-life insurance companies. The technical approach taken is to use B-splines to capture the underlying one-dimensional unspecified functions. It is shown via finite sample simulation studies and an application for forecasting future asbestos related deaths in the UK that the B-spline approach works well in practice. Special consideration has been given to ensure identifiability of all models considered

Coulomb corrections and multiple e+e- pair production in ultra-relativistic nuclear collisions

We consider the problem of Coulomb corrections to the inclusive cross section. We show that these corrections in the limiting case of small charge number of one of the nuclei coincide with those to the exclusive cross section. Within our approach we also obtain the Coulomb corrections for the case of large charge numbers of both nuclei.Comment: 7 pages, REVTeX

Relativistic r-modes in Slowly Rotating Neutron Stars: Numerical Analysis in the Cowling Approximation

We investigate the properties of relativistic $r$-modes of slowly rotating neutron stars by using a relativistic version of the Cowling approximation. In our formalism, we take into account the influence of the Coriolis like force on the stellar oscillations, but ignore the effects of the centrifugal like force. For three neutron star models, we calculated the fundamental $r$-modes with $l'=m=2$ and 3. We found that the oscillation frequency $\bar\sigma$ of the fundamental $r$-mode is in a good approximation given by $\bar\sigma\approx \kappa_0 \Omega$, where $\bar\sigma$ is defined in the corotating frame at the spatial infinity, and $\Omega$ is the angular frequency of rotation of the star. The proportional coefficient $\kappa_0$ is only weakly dependent on $\Omega$, but it strongly depends on the relativistic parameter $GM/c^2R$, where $M$ and $R$ are the mass and the radius of the star. All the fundamental $r$-modes with $l'=m$ computed in this study are discrete modes with distinct regular eigenfunctions, and they all fall in the continuous part of the frequency spectrum associated with Kojima's equation (Kojima 1998). These relativistic $r$-modes are obtained by including the effects of rotation higher than the first order of $\Omega$ so that the buoyant force plays a role, the situation of which is quite similar to that for the Newtonian $r$-modes.Comment: 22 pages, 8 figures, accepted for publication in Ap

Tunneling decay of false vortices

We consider the decay of vortices trapped in the false vacuum of a theory of scalar electrodynamics in 2+1 dimensions. The potential is inspired by models with intermediate symmetry breaking to a metastable vacuum that completely breaks a U(1) symmetry, while in the true vacuum the symmetry is unbroken. The false vacuum is unstable through the formation of true vacuum bubbles; however, the rate of decay can be extremely long. On the other hand, the false vacuum can contain metastable vortex solutions. These vortices contain the true vacuum inside in addition to a unit of magnetic flux and the appropriate topologically nontrivial false vacuum outside. We numerically establish the existence of vortex solutions which are classically stable; however, they can decay via tunneling. In general terms, they tunnel to a configuration which is a large, thin-walled vortex configuration that is now classically unstable to the expansion of its radius. We compute an estimate for the tunneling amplitude in the semi-classical approximation. We believe our analysis would be relevant to superconducting thin films or superfluids.Comment: 27 pages, 9 figure

The Battle of the Bulge: Decay of the Thin, False Cosmic String

We consider the decay of cosmic strings that are trapped in the false vacuum in a theory of scalar electrodynamics in 3+1 dimensions. We restrict our analysis to the case of thin-walled cosmic strings which occur when large magnetic flux trapped inside the string. Thus the string looks like a tube of fixed radius, at which it is classically stable. The core of the string contains magnetic flux in the true vacuum, while outside the string, separated by a thin wall, is the false vacuum. The string decays by tunnelling to a configuration which is represented by a bulge, where the region of true vacuum within, is ostensibly enlarged. The bulge can be described as the meeting, of a kink soliton anti-soliton pair, along the length of the string. It can be described as a bulge appearing in the initial string, starting from the string of small, classically stable radius, expanding to a fat string of large, classically unstable (to expansion) radius and then returning back to the string of small radius along its length. This configuration is the bounce point of a corresponding O(2) symmetric instanton, which we can determine numerically. Once the bulge appears it explodes in real time. The kink soliton anti-soliton pair recede from each other along the length of the string with a velocity that quickly approaches the speed of light, leaving behind a fat tube. At the same time the radius of the fat tube that is being formed, expands (transversely) as it is no longer classically stable, converting false vacuum to the true vacuum with ever diluting magnetic field within. The rate of this expansion is determined by the energy difference between the true vacuum and the false vacuum. Our analysis could be applied to a network, of cosmic strings formed in the very early universe or vortex lines in a superheated superconductor.Comment: 13 pages, 4 figure

Posterior consistency in linear models under shrinkage priors

We investigate the asymptotic behavior of posterior distributions of regression coefficients in high-dimensional linear models as the number of dimensions grows with the number of observations. We show that the posterior distribution concentrates in neighborhoods of the true parameter under simple sufficient conditions. These conditions hold under popular shrinkage priors given some sparsity assumptions.Comment: To appear in Biometrik

Alternative experimental evidence for chiral restoration in excited baryons

Given existing empirical spectral patterns of excited hadrons it has been suggested that chiral symmetry is approximately restored in excited hadrons at zero temperature/density (effective symmetry restoration). If correct, this implies that mass generation mechanisms and physics in excited hadrons is very different as compared to the lowest states. One needs an alternative and independent experimental information to confirm this conjecture. Using very general chiral symmetry arguments it is shown that strict chiral restoration in a given excited nucleon forbids its decay into the N \pi channel. Hence those excited nucleons which are assumed from the spectroscopic patterns to be in approximate chiral multiplets must only "weakly" decay into the N \pi channel, (f_{N^*N\pi}/f_{NN\pi})^2 << 1. However, those baryons which have no chiral partner must decay strongly with a decay constant comparable with f_{NN\pi}. Decay constants can be extracted from the existing decay widths and branching ratios. It turnes out that for all those well established excited nucleons which can be classified into chiral doublets N_+(1440) - N_-(1535), N_+(1710) - N_-(1650), N_+(1720) - N_-(1700), N_+(1680) - N_-(1675), N_+(2220) - N_-(2250), N_+(?) - N_-(2190), N_+(?) - N_-(2600), the ratio is (f_{N^*N\pi}/f_{NN\pi})^2 ~ 0.1 or much smaller for the high-spin states. In contrast, the only well established excited nucleon for which the chiral partner cannot be identified from the spectroscopic data, N(1520), has a decay constant into the N\pi channel that is comparable with f_{NN\pi}. This gives an independent experimental verification of the chiral symmetry restoration scenario.Comment: 4 pp. A new footnote with an alternative proof of impossibility of parity doublet decay into pi + N is added. To appear in Phys. Rev. Let

The triton and three-nucleon force in nuclear lattice simulations

We study the triton and three-nucleon force at lowest chiral order in pionless effective field theory both in the Hamiltonian and Euclidean nuclear lattice formalism. In the case of the Euclidean lattice formalism, we derive the exact few-body worldline amplitudes corresponding to the standard many-body lattice action. This will be useful for setting low-energy coefficients in future nuclear lattice simulations. We work in the Wigner SU(4)-symmetric limit where the S-wave scattering lengths {1}S{0} and {3}S{1} are equal. By comparing with continuum results, we demonstrate for the first time that the nuclear lattice formalism can be used to study few-body nucleon systems.Comment: 16 pages, 4 figure