Yulong Zhong | Searcharxiv

arXiv2026

Limiting absorption principle for time-harmonic acoustic and electromagnetic scattering of plane waves from a bi-periodic inhomogeneous layer

The Rayleigh expansion is widely used as a formal radiation condition in the analysis and numerical treatment of grating diffraction problems for incoming plane waves. However, the Rayleigh expansion does not always lead to uniqueness of open waveguide scattering problems, due to the existence of surface/guided waves (in other words, Bound States in the Continuum (BICs)) which exponentially decay in the direction perpendicular to the periodicity. In this paper we suppose that a bi-periodic inhomogeneous medium supports BICs at some real-valued incident wavenumber. Based on singular perturbation arguments, we justify the Limiting Absorption Principle (LAP) for both time-harmonic acoustic and electromagnetic scattering of plane waves from bi-periodic structures. Replacing the wavenumber $k$ with $k+iε$, we prove that the unique solution with $ε>0$ converges to a solution of the original diffraction problem that additionally satisfies an orthogonal identity. This constraint condition together with the classical Rayleigh expansion leads to a sharp radiation condition to ensure uniqueness of time-harmonic scattering of plane waves by BIC-supporting bi-periodic materials.

math.AP↗

arXiv2021

Improving prediction of the terrestrial water storage anomalies during the GRACE and GRACE-FO gap with Bayesian convolutional neural networks

The Gravity Recovery and Climate Experiment (GRACE) satellite and its successor GRACE Follow-On (GRACE-FO) provide valuable and accurate observations of terrestrial water storage anomalies (TWSAs) at a global scale. However, there is an approximately one-year observation gap of TWSAs between GRACE and GRACE-FO. This poses a challenge for practical applications, as discontinuity in the TWSA observations may introduce significant biases and uncertainties in the hydrological model predictions and consequently mislead decision making. To tackle this challenge, a Bayesian convolutional neural network (BCNN) driven by climatic data is proposed in this study to bridge this gap at a global scale. Enhanced by integrating recent advances in deep learning, including the attention mechanisms and the residual and dense connections, BCNN can automatically and efficiently extract important features for TWSA predictions from multi-source input data. The predicted TWSAs are compared to the hydrological model outputs and three recent TWSA prediction products. The comparison suggests the superior performance of BCNN in providing improved predictions of TWSAs during the gap in particular in the relatively arid regions. The BCNN's ability to identify the extreme dry and wet events during the gap period is further discussed and comprehensively demonstrated by comparing with the precipitation anomalies, drought index, ground/surface water levels. Results indicate that BCNN is capable of offering a reliable solution to maintain the TWSA data continuity and quantify the impacts of climate extremes during the gap.

physics.ao-ph↗