To model open-domain problems with Drude, Lorentz, and Debye media, the complex frequency-shifted perfectly matched layer (CFS-PML) is adopted to truncate the Crank-Nicolson Douglas-Gunn finite-difference time-domain (CNDG-FDTD) region. The auxiliary differential equation (ADE) and the bilinear Z-transform (BZT) methods are incorporated separately into the implementations of CNDG-CFS-PML formulations, while the ADE, piecewise linear recursive convolution (PLRC), and trapezoidal recursive convolution (TRC) methods are utilized to model dispersive media. The proposed formulations can not only circumvent the stability condition, but have the advantages of the CFS-PML in attenuating the evanescent waves and reducing the late-time reflection. Three numerical examples have been carried out to validate these formulations. The simulation results show that the proposed CNDG-CFS-PML algorithm is efficient in absorbing performance and saving more computational time compared with the conventional FDTD method, which leads to extensive applicability and acts as a very good prospect.
We systematically investigate ultrafast dynamic nonlinear mechanisms of photonic crystals (PhCs) with femtosecond (fs) pumping via the transmission change of a signal pulse. The pumping causes a nonlinear decrease (or increase) in the dielectric constant of the PhC material. A new phenomenon of the asymmetric change in the transmission spectra was observed in the gap region and the band-gap edge modes. For the band region, a sloped change in the transmission spectra was observed, and for the transition region, a hybrid of the two was observed. In addition, a universal dynamic picture of the fs nonlinear responses of the PhC was constructed.
The idea of causality has lasted for over thousands of years. Unlike the idea of statistical correlation and regression, performing causal modeling and prediction is an even more challenging job. Under the intervention framework of causality, causal modeling is gaining popularity given the advances of big data and computational ability in recent years. In different scientific research areas, there exist three powerful causal modeling methodologies, namely, the potential outcomes method in statistics, the instrumental variables method in economics and Judea Pearl’s causal diagram method (do-calculus) in computer science and artificial intelligence. In this paper, by linear causal modeling assumption, we prove that the above three causal methodologies are equivalent. That is, given a causal problem, all of the three modeling methods will generate the same causal relationship conclusion, despite that they own different causal inference processes. During the past one-and-half years, the global economy suffers severe impacts from the COVID-19 pandemic. To fight the deadly pandemic, various social distancing measures and actions, taken by the countries, are effective in curbing the impact of the pandemic over the population. However, such social distancing policy has an adverse effect over the global economy growth; if more stringent measures were taken, then there would be suffering in the forms of much slower economic growth and higher unemployment. In this paper, we study the causal relationships between social distancing, fatality rate and economy growth. This work provides a useful tool for the governments to keep balance between controlling the pandemic and maintaining economic growth.
We numerically investigate the ultrafast dynamic nonlinear mechanism of an Fabry-Perot (FP) cavity with femtosecond (fs) pumping by the transmission change of an incident signal pulse. The nonlinear effect simulated by a twolevel system model can decrease the dielectric constant. Therefore, the temporally transmitted pulse is compressed owing to the faster phase velocity, and a sloped change in the transmission spectra is observed, which can be explained by the mechanism of pulse deformation. In addition, we stretched a certain part of the temporally transmitted pulse to further demonstrate the deformation of the pulse mechanism. This dynamic nonlinear mechanism based on the FP cavity can not only be used to design new optical devices with ultrafast response times, such as pulse modulators and passive amplifiers, but can also be easily constructed and integrated, which has great practical applications.
This review provides available evidences that AIT, especially the treatment of LAK, can be used to decrease the early recurrence and mortality of postoperative HCC but may not the long term.
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