The detectability of single spinless stellar-mass black holes through gravitational lensing of gravitational waves with advanced LIGO

We investigate the detectability of gravitational waves that have been lensed by a spinless stellar-mass black hole, with respect to the advanced LIGO. By solving the full relativistic linear wave equations in the spacetime of a Schwarzschild black hole, we find that the strong gravity can create unique signals in the lensed waveform, particularly during the merger and ringdown stages. The differences in terms of fitting factor between the lensed waveform and best-fitted unlensed general relativity template with spin-precessing and higher-order multipoles are greater than $5\%$ for the lens black hole mass within $70M_{\odot}<M_{\rm lens}<133.33 M_{\odot}$ under advanced LIGO's sensitivity. This is up to 5 times more detectable than the previous analysis based on the weak field approximation for a point mass and covers most part of the black hole mass gap predicted by stellar evolution theory. Based on Bayesian inference, the lensing feature can be distinguished with a signal-to-noise ratio of 12.5 for $M_{\rm lens}=70 M_{\odot}$ and 19.2 for $M_{\rm lens}=250 M_{\odot}$, which is attainable for advanced LIGO.Comment: 6 pages, 5 figures, accepted for publication in PR

Estimation of Stator Resistance and Rotor Flux Linkage in SPMSM Using CLPSO with Opposition-Based-Learning Strategy

Electromagnetic parameters are important for controller design and condition monitoring of permanent magnet synchronous machine (PMSM) system. In this paper, an improved comprehensive learning particle swarm optimization (CLPSO) with opposition-based-learning (OBL) strategy is proposed for estimating stator resistance and rotor flux linkage in surface-mounted PMSM; the proposed method is referred to as CLPSO-OBL. In the CLPSO-OBL framework, an opposition-learning strategy is used for best particles reinforcement learning to improve the dynamic performance and global convergence ability of the CLPSO. The proposed parameter optimization not only retains the advantages of diversity in the CLPSO but also has inherited global exploration capability of the OBL. Then, the proposed method is applied to estimate the stator resistance and rotor flux linkage of surface-mounted PMSM. The experimental results show that the CLPSO-OBL has better performance in estimating winding resistance and PM flux compared to the existing peer PSOs. Furthermore, the proposed parameter estimation model and optimization method are simple and with good accuracy, fast convergence, and easy digital implementation

Simulating gravitational waves passing through the spacetime of a black hole

We investigate how GWs pass through the spacetime of a Schwarzschild black hole using time-domain numerical simulations. Our work is based on the perturbed 3+1 Einstein's equations up to the linear order. We show explicitly that our perturbation equations are covariant under infinitesimal coordinate transformations. Then we solve a symmetric second-order hyperbolic wave equation with a spatially varying wave speed. As the wave speed in our wave equation vanishes at the horizon, our formalism can naturally avoid boundary conditions at the horizon. Our formalism also does not contain coordinate singularities and, therefore, does not need regularity conditions. Then, based on our code, we simulate both finite and continuous initially plane-fronted wave trains passing through the Schwarzschild black hole. We find that for the finite wave train, the wave zone of GWs is wildly twisted by the black hole. While for the continuous wave train, unlike geometric optics, GWs can not be sheltered by the back hole. A strong beam and an interference pattern appear behind the black hole along the optical axis. Moreover, we find that the back-scattering due to the interaction between GWs and the background curvature is strongly dependent on the direction of the propagation of the trailing wavefront relative to the black hole.Comment: 24 pages, 9 figure

Revisiting f(R) gravity models that reproduce Λ\LambdaCDM expansion

We reconstruct an $f(R)$ gravity model that gives rise to the particular $\Lambda$CDM background evolution of the universe. We find well-defined, real-valued analytical forms for the $f(R)$ model to describe the universe both in the early epoch from the radiation to matter dominated eras and the late time acceleration period. We further examine the viability of the derived $f(R)$ model and find that it is viable to describe the evolution of the universe in the past and there does not exist the future singularity in the Lagrangian.Comment: 7 pages, 2 figures, revised version, accepted for publication in PR

Emergent Mott-insulators at non-integer fillings and devil's staircase induced by attractive interaction in many-body polarons

We investigate the ground state properties of an ultracold atom system consisting of many-body polarons, quasiparticles formed by impurity atoms in optical lattices immersing in a Bose-Einstein condensate. We find the nearest-neighbor attractive interaction between polarons can give rise to rich physics that is peculiar to this system. In a relatively shallow optical lattice, the attractive interaction can drive the system being in a self-bound superfluid phase with its particle density distribution manifesting a self-concentrated structure. While in a relatively deep optical lattice, the attractive interaction can drive the system forming the Mott-insulator phase even though the global filling factor is not integer. Interestingly, in the Mott-insulator regime, the system can support a series of different Mott-insulators with their effective density manifesting a devil's staircase structure with respect to the strength of attractive interaction. Detailed estimation on relevant experimental parameters shows that these rich physics can be readily observed in current experimental setups