Analytic properties of force-free jets in the Kerr spacetime -- III: uniform field solution

The structure of steady axisymmetric force-free magnetosphere of a Kerr black hole (BH) is governed by a second-order partial differential equation of $A_\phi$ depending on two "free" functions $\Omega(A_\phi)$ and $I(A_\phi)$, where $A_\phi$ is the $\phi$ component of the vector potential of the electromagnetic field, $\Omega$ is the angular velocity of the magnetic field lines and $I$ is the poloidal electric current. In this paper, we investigate the solution uniqueness. Taking asymptotically uniform field as an example, analytic studies imply that there are infinitely many solutions approaching uniform field at infinity, while only a unique one is found in general relativistic magnetohydrodynamic simulations. To settle down the disagreement, we reinvestigate the structure of the governing equation and numerically solve it with given constraint condition and boundary condition. We find that the constraint condition (field lines smoothly crossing the light surface (LS)) and boundary conditions at horizon and at infinity are connected via radiation conditions at horizon and at infinity, rather than being independent. With appropriate constraint condition and boundary condition, we numerically solve the governing equation and find a unique solution. Contrary to naive expectation, our numerical solution yields a discontinuity in the angular velocity of the field lines and a current sheet along the last field line crossing the event horizon. We also briefly discuss the applicability of the perturbation approach to solving the governing equation

Twist-3 contributions to γγ→π+π−,K+K−\gamma\gamma\rightarrow\pi^+\pi^-,K^+K^- processes in perturbative QCD approach

As one of the simplest hadronic processes, $\gamma\gamma\rightarrow M^{+}M^{-}$ ($M=\pi,K$) could be a good testing ground for our understanding of the perturbative and nonperturbative structure of QCD, and will be studied with high precision at BELLE-\RNum{2} in the near future. In this paper, we revisit these processes with twist-3 corrections in the perturbative QCD approach based on the $k_{T}$ factorization theorem, in which transverse degrees of freedom as well as resummation effects are taken into account. The influence of the distribution amplitudes on the cross sections are discussed in detail. Our work shows that not only the transverse momentum effects but also the twist-3 corrections play a significant role in the processes $\gamma\gamma\rightarrow M^{+}M^{-}$ in the intermediate energy region. Especially in the few GeV region, the twist-3 contributions become dominant in the cross sections. And it is noteworthy that both the twist-3 result of the $\pi^{+}\pi^{-}$ cross section and that of the $K^{+}K^{-}$ cross section agree well with the BELLE and ALEPH measurements. For the pion and kaon angular distributions, there still exist discrepancies between our results and the experimental measurements. Possible reasons for these discrepancies are discussed briefly.Comment: 19 pages, 7 figures and 2 tables. Contents improved and more discussions adde

Artificial-Noise-Aided Physical Layer Phase Challenge-Response Authentication for Practical OFDM Transmission

Recently, we have developed a PHYsical layer Phase Challenge-Response Authentication Scheme (PHY-PCRAS) for independent multicarrier transmission. In this paper, we make a further step by proposing a novel artificial-noise-aided PHY-PCRAS (ANA-PHY-PCRAS) for practical orthogonal frequency division multiplexing (OFDM) transmission, where the Tikhonov-distributed artificial noise is introduced to interfere with the phase-modulated key for resisting potential key-recovery attacks whenever a static channel between two legitimate users is unfortunately encountered. Then, we address various practical issues for ANA-PHY-PCRAS with OFDM transmission, including correlation among subchannels, imperfect carrier and timing recoveries. Among them, we show that the effect of sampling offset is very significant and a search procedure in the frequency domain should be incorporated for verification. With practical OFDM transmission, the number of uncorrelated subchannels is often not sufficient. Hence, we employ a time-separated approach for allocating enough subchannels and a modified ANA-PHY-PCRAS is proposed to alleviate the discontinuity of channel phase at far-separated time slots. Finally, the key equivocation is derived for the worst case scenario. We conclude that the enhanced security of ANA-PHY-PCRAS comes from the uncertainty of both the wireless channel and introduced artificial noise, compared to the traditional challenge-response authentication scheme implemented at the upper layer.Comment: 33 pages, 13 figures, submitted for possible publicatio

A Novel Location Free Link Prediction in Multiplex Social Networks

In recent decades, the emergence of social networks has enabled internet service providers (e.g., Facebook, Twitter and Uber) to achieve great commercial success. Link prediction is recognized as a common practice to build the topology of social networks and keep them evolving. Conventionally, link prediction methods are dependent of location information of users, which suffers from information leakage from time to time. To deal with this problem, companies of smart devices (e.g., Apple Inc.) keeps tightening their privacy policy, impeding internet service providers from acquiring location information. Therefore, it is of great importance to design location free link prediction methods, while the accuracy still preserves. In this study, a novel location free link prediction method is proposed for complex social networks. Experiments on real datasets show that the precision of our location free link prediction method increases by 10 percent

Caring for grandchildren and intergenerational support in rural China: a gendered extended family perspective

This investigation examines how support from adult children is affected by their parents’ involvement in grandchild care. Instead of focusing on dyadic interactions, we adopt a gendered extended family perspective to examine how financial and emotional support from children was influenced when their siblings received help with child care from their elder parents. The data were from a two-wave (2001, 2003) longitudinal study of 4,791 parent–child dyads with 1,162 parents, aged 60 and older, living in rural areas of Anhui Province, China. Random effects regression showed that emotional support from both sons and daughters was strengthened when parents provided more child care for their other adult children; in addition, daughters were more emotionally responsive than sons under this situation. Concerning dyadic parent–child relationships, daughter and sons increased their financial support, and sons increased their emotional support when they themselves received help with child care from parents. We suggest taking a gendered extended family perspective when studying intergenerational relationships in rural China

Demonstration of the double Q^2-rescaling model

In this paper we have demonstrated the double Q^2-rescaling model (DQ^2RM) of parton distribution functions of nucleon bounded in nucleus. With different x-region of l-A deep inelastic scattering process we take different approach: in high x-region (0.1\le x\le 0.7) we use the distorted QCD vacuum model which resulted from topologically multi -connected domain vacuum structure of nucleus; in low x-region (10^{-4}\le x\le10^{-3}) we adopt the Glauber (Mueller) multi- scattering formula for gluon coherently rescattering in nucleus. From these two approach we justified the rescaling parton distribution functions in bound nucleon are in agreement well with those we got from DQ^2RM, thus the validity for this phenomenologically model are demonstrated.Comment: 19 page, RevTex, 5 figures in postscrip