Collective modes of a harmonically trapped one-dimensional Bose gas: the effects of finite particle number and nonzero temperature

Following the idea of the density functional approach, we develop a generalized Bogoliubov theory of an interacting Bose gas confined in a one-dimensional harmonic trap, by using a local chemical potential - calculated with the Lieb-Liniger exact solution - as the exchange energy. At zero temperature, we use the theory to describe collective modes of a finite-particle system in all interaction regimes from the ideal gas limit, to the mean-field Thomas-Fermi regime, and to the strongly interacting Tonks-Girardeau regime. At finite temperature, we investigate the temperature dependence of collective modes in the weak-coupling regime by means of a Hartree-Fock-Bogoliubov theory with Popov approximation. By emphasizing the effects of finite particle number and nonzero temperature on collective mode frequencies, we make comparisons of our results with the recent experimental measurement [E. Haller et al., Science 325, 1224 (2009)] and some previous theoretical predictions. We show that the experimental data are still not fully explained within current theoretical framework.Comment: 10 pages, 8 figure

In Search of ‘Taiwaneseness’ – Reconsidering Taiwanese Xing-ju from a Post-colonial Perspective

Xing-ju literally means ‘New Theatre’ in mandarin and denotes the non-traditional performing style in Taiwan. Xing-ju is regarded as the product of colonisation in Taiwan. The thesis began with the first emergence of Xing-ju in the Japanese colonial era at the beginning of the twentieth century, and went on to examine the development of Xing-ju and its sub-forms within a colonial historical context. Having gone through different colonial regimes, Xing-ju has developed into the local theatre form characterizing the hybridity of Taiwanese culture. My study aims to fill a gap in Taiwanese contemporary theatre history, to look at Xing-ju and its sub-forms from a post-colonial perspective, and to provide a continuous and complete Xing-ju history within a theoretical context. In addition, how Xing-ju has exemplified ‘Taiwaneseness’ while presenting multiple cultural characteristics is also examined. This thesis also draws on primary source data, obtained via field research, to analyse the characteristics of Xing-ju performances. Finally, while addressing my research questions through theoretical analysis, I also examine them through the lens of practical work. Inspired by critical syncretism, I experiment with an alternative way to explore the nature of Taiwanese culture and theatre form. With its hybrid cultural characteristics including Japanese Shinpa-geki, Chinese Peking Opera, Ge-zai Xi and Western theatre styles, I discuss how a definition of ‘Taiwaneseness’ emerges through Xing-ju.Taiwan Ministry of Educatio

Cosmological application of the lens-redshift probability distribution with improved galaxy-scale gravitational lensing sample

We conduct the cosmological analysis by using the lens-redshift distribution test with updated galaxy-scale strong lensing sample, where the considered scenarios involve three typical cosmological models (i.e., $\Lambda$CDM, $\omega$CDM and $\omega_0\omega_a$CDM models) and three typical choices (i.e., non-evolving, power-law and exponential forms) for the velocity-dispersion distribution function (VDF) of lens galaxies. It shows that degeneracies between cosmological and VDF parameters lead to the shifts of estimates on the parameters. The limits on $\Omega_{m0}$ from the lens-redshift distribution are consistent with those from the Pantheon+ Type Ia supernova (SN Ia) sample at 68.3% confidence level, though the uncertainties on $\Omega_{m0}$ from the former are about 3 to 8 times larger than those from the latter. The mean values of $\Omega_{m0}$ shift to the larger values in the power-law VDF case and to the lower values in the exponential VDF case, compared with those obtained in the non-evolving VDF case. In the $\omega$CDM model, the limits on $\omega_0$, i.e. the dark energy equation of state (EoS), are consistent with those from the Pantheon+ sample at 68.3% confidence level, but the mean values of $\omega_0$ from the former are significantly smaller than those from the latter. In the $\omega_0\omega_a$CDM model, the uncertainties on $\omega_0$ are dramatically enlarged compared with those obtained in the $\omega$CDM model; moreover, the Markov chains of $\omega_a$, i.e. the time-varying slope of EoS, do not achieve convergence in the three VDF cases. Overall, the lens-redshift distribution test is more effective on constraining $\Omega_{m0}$ than on the dark energy EoS.Comment: 10 pages, 3 figures, 1 tabl

An evolutionary algorithm with double-level archives for multiobjective optimization

Existing multiobjective evolutionary algorithms (MOEAs) tackle a multiobjective problem either as a whole or as several decomposed single-objective sub-problems. Though the problem decomposition approach generally converges faster through optimizing all the sub-problems simultaneously, there are two issues not fully addressed, i.e., distribution of solutions often depends on a priori problem decomposition, and the lack of population diversity among sub-problems. In this paper, a MOEA with double-level archives is developed. The algorithm takes advantages of both the multiobjective-problemlevel and the sub-problem-level approaches by introducing two types of archives, i.e., the global archive and the sub-archive. In each generation, self-reproduction with the global archive and cross-reproduction between the global archive and sub-archives both breed new individuals. The global archive and sub-archives communicate through cross-reproduction, and are updated using the reproduced individuals. Such a framework thus retains fast convergence, and at the same time handles solution distribution along Pareto front (PF) with scalability. To test the performance of the proposed algorithm, experiments are conducted on both the widely used benchmarks and a set of truly disconnected problems. The results verify that, compared with state-of-the-art MOEAs, the proposed algorithm offers competitive advantages in distance to the PF, solution coverage, and search speed

Bi-velocity discrete particle swarm optimization and its application to multicast routing problem in communication networks

This paper proposes a novel bi-velocity discrete particle swarm optimization (BVDPSO) approach and extends its application to the NP-complete multicast routing problem (MRP). The main contribution is the extension of PSO from continuous domain to the binary or discrete domain. Firstly, a novel bi-velocity strategy is developed to represent possibilities of each dimension being 1 and 0. This strategy is suitable to describe the binary characteristic of the MRP where 1 stands for a node being selected to construct the multicast tree while 0 stands for being otherwise. Secondly, BVDPSO updates the velocity and position according to the learning mechanism of the original PSO in continuous domain. This maintains the fast convergence speed and global search ability of the original PSO. Experiments are comprehensively conducted on all of the 58 instances with small, medium, and large scales in the OR-library (Operation Research Library). The results confirm that BVDPSO can obtain optimal or near-optimal solutions rapidly as it only needs to generate a few multicast trees. BVDPSO outperforms not only several state-of-the-art and recent heuristic algorithms for the MRP problems, but also algorithms based on GA, ACO, and PSO