Numerical methods and comparison for the Dirac equation in the nonrelativistic limit regime

We analyze rigorously error estimates and compare numerically spatial/temporal resolution of various numerical methods for the discretization of the Dirac equation in the nonrelativistic limit regime, involving a small dimensionless parameter $0<\varepsilon\ll 1$ which is inversely proportional to the speed of light. In this limit regime, the solution is highly oscillatory in time, i.e. there are propagating waves with wavelength $O(\varepsilon^2)$ and $O(1)$ in time and space, respectively. We begin with several frequently used finite difference time domain (FDTD) methods and obtain rigorously their error estimates in the nonrelativistic limit regime by paying particular attention to how error bounds depend explicitly on mesh size $h$ and time step $\tau$ as well as the small parameter $\varepsilon$. Based on the error bounds, in order to obtain `correct' numerical solutions in the nonrelativistic limit regime, i.e. $0<\varepsilon\ll 1$, the FDTD methods share the same $\varepsilon$-scalability on time step: $\tau=O(\varepsilon^3)$. Then we propose and analyze two numerical methods for the discretization of the Dirac equation by using the Fourier spectral discretization for spatial derivatives combined with the exponential wave integrator and time-splitting technique for temporal derivatives, respectively. Rigorous error bounds for the two numerical methods show that their $\varepsilon$-scalability on time step is improved to $\tau=O(\varepsilon^2)$ when $0<\varepsilon\ll 1$. Extensive numerical results are reported to support our error estimates.Comment: 34 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1511.0119

Map kinase phosphatase 2 regulates macrophage-adipocyte interaction

PLoS ONE103e012075

Financial wealth, socioemotional wealth, and founder exits: an empirical examination of Chinese IPOs

Initial public offerings (IPOs) are typically viewed as the peak of entrepreneurial success, providing founder-CEOs a chance to profitably exit. Founder-CEOs, however, are often motivated by non-financial considerations in addition to the desire to amass wealth. According to the behavioral agency model, the founder-CEOs’ framing of gains vs. losses of their wealth creation at IPO determines their risk aversion vs. risk taking behaviors. In addition, the behavioral agency model argues that founder-CEOs with a great deal of socioemotional wealth fear losing that wealth. This fear will attenuate their aversion to losing financial wealth. To test our model, we collected a sample of 130 entrepreneurial IPOs from 2004 to 2009 in China whose founder-CEOs left the firm after it went public. The results confirm a U-shaped relationship between the founder-CEOs’ financial wealth and their exit speed after the IPO. A high level of socioemotional wealth, exemplified by the CEOs’ tenure, a higher ratio of insiders on the board, and the age of the stock market, negatively moderates the effect of financial wealth. We contribute to the literature by providing empirical support for the behavioral agency model and founder-CEO exits in China by examining both financial and socioemotional wealth.publishedVersio

Bimetallic FeOₓ–MOₓ Loaded TiO₂ (M = Cu, Co) Nanocomposite Photocatalysts for Complete Mineralization of Herbicides

A series of monometallic and bimetallic cocatalyst(s), comprising FeOx, CuOx, CoOx, FeOx–CuOx, and FeOx–CoOx loaded TiO2 catalysts prepared by the surface impregnation method, were investigated for the photocatalytic mineralization of the widely used four herbicides: 2,4-dichlorophenol (2,4-DCP), 2,4,6-trichlorophenol (2,4,6-TCP), 2,4-dichlorophenoxyacetic acid (2,4-D), and 2,4,5-trichlorophenoxyacetic acid (2,4,5-T). It was found that FeOx–CoOx/TiO2 showed the highest photocatalytic efficiency toward mineralization of selected herbicides. FeOx–CoOx/TiO2 achieves 92% TOC removal in 180 min, representing nearly three time activity of the benchmark PC50 TiO2. From XPS analysis, FeOOH, CuO, and CoO were determined to be loaded onto the TiO2 surface. The outstanding photocatalytic performance of the optimized FeOx–CoOx/TiO2 sample for herbicides mineralization is due to an increased charge separation and enhanced hydroxyl radicals production monitored by diverse spectroscopies. Based on the proposed charge transfer mechanism, FeOx–CoOx cocatalyst species accelerate the transfer of photogenerated holes on TiO2, thus facilitating hydroxyl radicals production

EFFECT OF MINDFULNESS-BASED STRESS REDUCTION THERAPY ON WORK STRESS AND MENTAL HEALTH OF PSYCHIATRIC NURSES

Background: Psychiatric nurses are a special group of nursing staff, they experience greater work stress and lower mental health levels than regular nurses. In order to address this problem, the effect of mindfulness-based stress reduction (MBSR) therapy on work stress and mental health of psychiatric nurses is investigated in this study. Subjects and methods: From August 2017 to November 2017, 100 psychiatric nurses, including 68 females and 32 males, were selected as participants from three hospitals in Hunan Province of China. They were randomly divided into the intervention and control groups, with 50 respondents in each group. MBSR therapy was used as psychological intervention in the intervention group. Before and after the intervention, the two groups were assessed with the Symptom Checklist-90 (SCL-90) scale, Self-Rating Depression Scale (SDS), Self-Rating Anxiety Scale (SAS), and Nursing Stress Scale. Results: (1) After the intervention, the SCL-90 score of the intervention group decrease significantly, and a statistically significant difference is observed with the figure before the intervention (P<0.001). No statistically significant difference is found in the control group (P>0.05). (2) After the intervention, the SDS and SAS scores of the intervention group decrease significantly, and a statistically significant difference is observed with the figures before the intervention (P<0.001). No statistically significant difference is found in the control group (P>0.05). (3) After the intervention, the Nursing Stress Scale score of the intervention group Nursing Stress Scale decrease significantly, and a statistically significant difference is observed with the figure before the intervention (P0.05). Conclusions: MBSR therapy can reduce work stress, anxiety, depression, and other negative emotions among psychiatric nurses and improve their mental health

Crack propagation in brittle solid containing 3D surface fracture under uniaxial compression

2003-2004 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Progress and challenges in photocatalytic ammonia synthesis

Photocatalytic ammonia (NH_{3}) synthesis from N_{2} and water driven by solar energy is a sustainable and environmentally friendly technology, which has gained considerable attention in recent years. In this review, the recent development in the fundamental understanding of photocatalytic NH_{3} synthesis and the methods of precise NH_{3} detection are summarized. More importantly the strategy for surface engineering and interface engineering of photocatalysts toward photocatalytic NH_{3} production has been thoroughly analyzed with the aim to stimulate critical thinking about the effective methodology for catalyst modification instead of exploring new materials. At the end the challenges and a few concerns are raised from the current reports and future perspectives in this research field are discussed targeting to clarify the reliability and reproducibility of the photochemical process and to direct the future research direction, such as flow reactor design and in-depth understanding of the underlying reaction pathway