Spectral properties, generation order parameters and luminosities for spin-powered X-ray pulsars

We show the spectral properties of 15 spin-powered X-ray pulsars, and the correlation between the average power-law photon index and spin-down rate. Generation order parameters (GOPs) based on polar-cap models are introduced to characterize the X-ray pulsars. We calculate three definitions of generation order parameters due to the different effects of magnetic and electric fields on photon absorption during cascade processes, and study the relations between the GOPs and spectral properties of X-ray pulsars. There exists a possible correlation between the photon index and GOP in our pulsar sample. Furthermore, we present a method due to the concept of GOPs to estimate the non-thermal X-ray luminosity for spin-powered pulsars. Then X-ray luminosity is calculated in the context of our polar-cap accelerator model which is well consistent with the most observed X-ray pulsar data. The ratio between X-ray luminosity estimated by our method and the pulsar's spin-down power is well consistent with the $L_{\rm X}\sim 10^{-3}L_{\rm sd}$ feature.Comment: 20 pages, 8 figures, 1 table, revised version for the publication in Ap

Tracking Nonlinear Correlation for Complex Dynamic Systems Using a Windowed Error Reduction Ratio Method

Studying complex dynamic systems is usually very challenging due to limited prior knowledge and high complexity of relationships between interconnected components. Current methods either are like a “black box” that is difficult to understand and relate back to the underlying system or have limited universality and applicability due to too many assumptions. This paper proposes a time-varying Nonlinear Finite Impulse Response model to estimate the multiple features of correlation among measurements including direction, strength, significance, latency, correlation type, and nonlinearity. The dynamic behaviours of correlation are tracked through a sliding window approach based on the Blackman window rather than the simple truncation by a Rectangular window. This method is particularly useful for a system that has very little prior knowledge and the interaction between measurements is nonlinear, time-varying, rapidly changing, or of short duration. Simulation results suggest that the proposed tracking approach significantly reduces the sensitivity of correlation estimation against the window size. Such a method will improve the applicability and robustness of correlation analysis for complex systems. A real application to environmental changing data demonstrates the potential of the proposed method by revealing and characterising hidden information contained within measurements, which is usually “invisible” for conventional methods

Far-infrared study of K giants in the solar neighborhood: Connection between Li enrichment and mass-loss

We searched for a correlation between the two anomalous properties of K giants: Li enhancement and IR excess from an unbiased survey of a large sample of RGB stars. A sample of 2000 low-mass K giants with accurate astrometry from the Hipparcos catalog was chosen for which Li abundances have been determined from low-resolution spectra. Far-infrared data were collected from the $WISE$ and $IRAS$ catalogs. To probe the correlation between the two anomalies, we supplemented 15 Li-rich K giants discovered from this sample with 25 known Li-rich K giants from other studies. Dust shell evolutionary models and spectral energy distributions were constructed using the code DUSTY to estimate different dust shell properties, such as dust evolutionary time scales, dust temperatures, and mass-loss rates. Among 2000 K giants, we found about two dozen K giants with detectable far-IR excess, and surprisingly, none of them are Li-rich. Similarly, the 15 new Li-rich K giants that were identified from the same sample show no evidence of IR excess. Of the total 40 Li-rich K giants, only 7 show IR excess. Important is that K giants with Li enhancement and/or IR excess begin to appear only at the bump on the RGB. Results show that K giants with IR excess are very rare, similar to K giants with Li enhancement. This may be due to the rapid differential evolution of dust shell and Li depletion compared to RGB evolutionary time scales. We also infer from the results that during the bump evolution, giants probably undergo some internal changes, which are perhaps the cause of mass-loss and Li-enhancement events. However, the available observational results do not ascertain that these properties are correlated. That a few Li-rich giants have IR excess seems to be pure coincidence.Comment: Accepted for Publication in Astronomy & Astrophysics, 6 figures, 5 tables, 19 page

Lowest eigenvalue of the nuclear shell model Hamiltonian

In this paper we investigate regular patterns of matrix elements of the nuclear shell model Hamiltonian $H$, by sorting the diagonal matrix elements from the smaller to larger values. By using simple plots of non-zero matrix elements and lowest eigenvalues of artificially constructed "sub-matrices" $h$ of $H$, we propose a new and simple formula which predicts the lowest eigenvalue with remarkable precisions.Comment: six pages, four figures, Physical Review C, in pres

A New Kind of Uniformly Accelerated Reference Frames

A new kind of uniformly accelerated reference frames with a line-element different from the M{\o}ller and Rindler ones is presented, in which every observer at $x, y, z=$consts. has the same constant acceleration. The laws of mechanics are checked in the new kind of frames. Its thermal property is studied. The comparison with the M{\o}ller and Rindler uniform accelerated reference frames is also made.Comment: 10 pages, 2 figures. to appear in Int. J. Mod. Phys.

Ballistic thermal conductance limited by phonon roughness scattering: A comparison of power-law and Gaussian roughness

In this work, we have investigated the influence of power-law roughness on the ballistic thermal conductance KTH for a nanosized beam adiabatically connected between two heat reservoirs. The sideways wall beam roughness is assumed to be power-law type, which is described by the roughness amplitude w, the in-plane roughness correlation length ξ and the roughness exponent 0≤H≤1. Distinct differences occur in between power-law and Gaussian wall roughness. For power-law roughness with low roughness exponents H (<0.5), the influence of phonon scattering can be rather destructive leading to significant deviations from the universal conductance value for flat beam walls. On the other hand for large roughness exponents (H>0.5) the conductance drop is significantly smaller than that of Gaussian roughness assuming similar roughness ratios w/ξ.