Exact solutions to the three-dimensional Gross-Pitaevskii equation with modulated radial nonlinearity

We study the Bose-Einstein condensate trapped in a three-dimensional spherically symmetrical potential. Exact solutions to the stationary Gross-Pitaevskii equation are obtained for properly modulated radial nonlinearity. The solutions contain vortices with different winding numbers and exhibit the shell-soliton feature in the radial distributions.Comment: 5 figure

Derivations and automorphisms of twisted deformative Schr\"{o}dinger-Virasoro Lie algebras

In this paper the derivation algebra and automorphism group of the twisted deformative Schr\"{o}dinger-Virasoro Lie algebras are determined.Comment: 25 page

Study of Decay Modes B -->K_0^*(1430) phi

Within the framework of perturbative QCD approach based on $\mathbf{k_T}$ factorization, we investigate the charmless decay mode $B \to K_0^*(1430)\phi$. Under two different scenarios (S1 and S2) for the description of scalar meson $K_0^*(1430)$, we explore the branching fractions and related CP asymmetries. Besides the dominant contributions from the factorizable emission diagrams, penguin operators in the annihilation diagrams could also provide considerable contributions. The central values of our predictions are larger than those from the QCD factorization in both scenarios. Compared with the experimental measurements of the BaBar collaboration, the result of neutral channel in the S1 agrees with experimental data, while the result of the charged one is a bit smaller than the data. In the S2 scenario, although the central value for the branching fractions of both channels are much larger than the data, the predictions could agree with the data due to the large uncertainties to the branching fractions from the hadronic input parameters. The CP asymmetry in the charged channel is small and not sensitive to CKM angle $\gamma$. With the accurate data in near future from the various $B$ factories, these predictions will be under stringent tests.Comment: 15 pages, 4 figure

Study of Magnetic Hysteresis Effects in a Storage Ring Using Precision Tune Measurement

With advances in accelerator science and technology in the recent decades, the accelerator community has focused on the development of next-generation light sources, for example the diffraction-limited storage rings (DLSRs), which requires precision control of the electron beam energy and betatron tunes. This work is aimed at understanding magnet hysteresis effects on the electron beam energy and lattice focusing in the circular accelerators, and developing new methods to gain better control of these effects. In this paper, we will report our recent experimental study of the magnetic hysteresis effects and their impacts on the Duke storage ring lattice using the transverse feedback based precision tune measurement system. The major magnet hysteresis effects associated with magnet normalization and lattice ramping are carefully studied to determine an effective procedure for lattice preparation while maintaining a high degree of reproducibility of lattice focusing. The local hysteresis effects are also studied by measuring the betatron tune shifts resulted from adjusting the setting of a quadrupole. A new technique has been developed to precisely recover the focusing strength of the quadrupole by returning it to a proper setting to overcome the local hysteresis effect

Hierarchically Structured Meta-learning

In order to learn quickly with few samples, meta-learning utilizes prior knowledge learned from previous tasks. However, a critical challenge in meta-learning is task uncertainty and heterogeneity, which can not be handled via globally sharing knowledge among tasks. In this paper, based on gradient-based meta-learning, we propose a hierarchically structured meta-learning (HSML) algorithm that explicitly tailors the transferable knowledge to different clusters of tasks. Inspired by the way human beings organize knowledge, we resort to a hierarchical task clustering structure to cluster tasks. As a result, the proposed approach not only addresses the challenge via the knowledge customization to different clusters of tasks, but also preserves knowledge generalization among a cluster of similar tasks. To tackle the changing of task relationship, in addition, we extend the hierarchical structure to a continual learning environment. The experimental results show that our approach can achieve state-of-the-art performance in both toy-regression and few-shot image classification problems.Comment: ICML 2019; Errata: this version fix the results of A1 in Table 1

Fixed-Symbol Aided Random Access Scheme for Machine-to-Machine Communications

The massiveness of devices in crowded Machine-to-Machine (M2M) communications brings new challenges to existing random-access (RA) schemes, such as heavy signaling overhead and severe access collisions. In order to reduce the signaling overhead, we propose a fixed-symbol aided RA scheme where active devices access the network in a grant-free method, i.e., data packets are directly transmitted in randomly chosen slots. To further address the access collision which impedes the activity detection, one fixed symbol is inserted into each transmitted data packet in the proposed scheme. An iterative message passing based activity detection (MP-AD) algorithm is performed upon the received signal of this fixed symbol to detect the device activity in each slot. In addition, the deep neural network-aided MP-AD (DNN-MP-AD) algorithm is further designed to alleviate the correlation problem of the iterative message passing process. In the DNN-MP-AD algorithm, the iterative message passing process is transferred from a factor graph to a DNN. Weights are imposed on the messages in the DNN and further trained to improve the accuracy of the device activity detection. Finally, numerical simulations are provided for the throughput of the proposed RA scheme, the accuracy of the proposed MP-AD algorithm, as well as the improvement brought by the DNN-MP-AD algorithm.Comment: 15 pages, 9 figure

Compensation for Booster Leakage Field in the Duke Storage Ring

The High Intensity Gamma-ray Source (HIGS) at Duke University is an accelerator-driven Compton gamma-ray source, providing high flux gamma-ray beam from 1 MeV to 100 MeV for photo-nuclear physics research. The HIGS facility operates three accelerators, a linac pre-injector (0.16 GeV), a booster injector (0.16-1.2 GeV), and an electron storage ring (0.24-1.2 GeV). Because of proximity of the booster injector to the storage ring, the magnetic field of the booster dipoles close to the ring can significantly alter the closed orbit in the storage ring being operated in the low energy region. This type of orbit distortion can be a problem for certain precision experiments which demand a high degree of the energy consistency of the gamma-ray beam. This energy consistency can be achieved by maintaining consistent aiming of the gamma-ray beam, therefore, a steady electron beam orbit and angle at the Compton collision point. To overcome the booster leakage field problem, we have developed an orbit compensation scheme. This scheme is developed using two fast orbit correctors and implemented as a feedforward which is operated transparently together with the slow orbit feedback system. In this paper, we will describe the development of this leakage field compensation scheme, and report the measurement results which have demonstrated the effectiveness of the scheme

Can scaling analysis be used to interpret the anti-parity-time symmetry in heat transfer?

In a previous work (Li et al. Science 364, 170) [1], we proposed a heat transfer system that preserves the anti-parity-time (APT) symmetry, and observe the rest-to-motion phase transition during the symmetry breaking. Recently, it was suggested (Zhao et al. arXiv:1906.08431) [2] that the behaviours of the system can be understood using scaling analysis based on the P\'eclet and Nusselt numbers (Pe and Nu). It was further proposed that there exists a third regime in the phase diagram in addition to the symmetric and symmetry broken phases. Although we appreciate the proposal to characterize the contributions of coupling, diffusion, and advection with dimensionless numbers, here we show that they do not help to predict or interpret the behaviours of the APT system. The dimensionless numbers do not provide enough details about the system to conclude that there is a motionless phase, a phase transition, to find the critical point, or to give the correct phase diagram with only two regimes

Breather induced quantized superfluid vortex filaments and their characterization

We study and characterize the breather-induced quantized superfluid vortex filaments which correspond to the Kuznetsov-Ma breather and super-regular breather excitations developing from localised perturbations. Such vortex filaments, emerging from an otherwise perturbed helical vortex, exhibit intriguing loop structures corresponding to the large amplitude of breathers due to the dual action of bending and twisting of the vortex. The loop induced by Kuznetsov-Ma breather emerges periodically as time increases, while the loop structure triggered by super-regular breather---the loop pair---exhibits striking symmetry breaking due to the broken reflection symmetry of the group velocities of super-regular breather. In particular, we identify explicitly the generation conditions of these loop excitations by introducing a physical quantity---the integral of the relative quadratic curvature---which corresponds to the effective energy of breathers. Although the nature of nonlinearity, it is demonstrated that this physical quantity shows a linear correlation with the loop size. These results will deepen our understanding of breather-induced vortex filaments and be helpful for controllable ring-like excitations on the vortices.Comment: 9 pages, 9 figure

Joint Uplink and Downlink Relay Selection in Cooperative Cellular Networks

We consider relay selection technique in a cooperative cellular network where user terminals act as mobile relays to help the communications between base station (BS) and mobile station (MS). A novel relay selection scheme, called Joint Uplink and Downlink Relay Selection (JUDRS), is proposed in this paper. Specifically, we generalize JUDRS in two key aspects: (i) relay is selected jointly for uplink and downlink, so that the relay selection overhead can be reduced, and (ii) we consider to minimize the weighted total energy consumption of MS, relay and BS by taking into account channel quality and traffic load condition of uplink and downlink. Information theoretic analysis of the diversity-multiplexing tradeoff demonstrates that the proposed scheme achieves full spatial diversity in the quantity of cooperating terminals in this network. And numerical results are provided to further confirm a significant energy efficiency gain of the proposed algorithm comparing to the previous best worse channel selection and best harmonic mean selection algorithms.Comment: Accepted by VTC-2010FAL