When using spectral methods, a consistent method for tuning the expansion order is often required, especially for time-dependent problems in which oscillations emerge in the solution. In this paper, we propose a frequency-dependent p-adaptive technique that adaptively adjusts the expansion order based on a frequency indicator. Using this p-adaptive technique, combined with recently proposed scaling and moving techniques, we are able to devise an adaptive spectral method in unbounded domains that can capture and handle diffusion, advection, and oscillations. As an application, we use this adaptive spectral method to numerically solve Schrödinger’s equation in an unbounded domain and successfully capture the solution’s oscillatory behavior at infinity.
To distinctively identify two objects at the deep-subwavelength scales requires sharp superfocusing to overcome the diffraction limit. However, conventional superfocusing effect and information-carrying capacity are limited by the focal length and single focusing field (only electric or magnetic field), which are hard to be apparently improved. Here, we introduce the concept of “dual-foci superfocusing”, an advanced focusing form that can provide either one or two focusing spots, simultaneously converging both electric and magnetic fields and presenting an effect of electromagnetostatic space-division multiplexing. The physical mechanism of the dual-foci superfocusing is analyzed and synthesized by an original theory of shaping functional fields using hybrid-magnitude evanescent modes. Through a terahertz plasmonic array, the dual-foci superfocusing is numerically demonstrated, whose metric (ratio of focal length to focusing-spot size) is sufficiently improved from traditional 1–1.8 up to 2.8. The proposed methodology could be exploited as a platform to investigate the novel concurrent characteristics of superfocusing and might represent an important step toward the development of beam manipulation and sophisticated holography.
Microfluidic droplets are widely applied in various fields such as biomedicine, aerospace, energy utilization, and chemical engineering due to their advantages of large specific surface area, uniform size, stability, and easy control. The double T-shaped microchannel has the characteristics of rapid preparation of microdroplets with controllable size and good uniformity. Through 3D numerical simulation, the influence of the constriction structure of the microchannel on the formation of droplets was studied qualitatively and quantitatively. Compared with ordinary double T-shaped microchannels, the microchannels with a necked structure generate smaller droplets in diameter and faster generation frequency. Among the three structures of rectangular necking, inverted trapezoidal necking, and trapezoidal necking, the microchannel with the latter structure has the best performance, can produce monodisperse droplets of uniform size, and the period is stable.