scholarly journals Realization of Second-Order Photonic Square-Root Topological Insulators

ACS Photonics ◽  
2021 ◽  
Author(s):  
Wenchao Yan ◽  
Daohong Song ◽  
Shiqi Xia ◽  
Junfang Xie ◽  
Liqin Tang ◽  
...  
Keyword(s):  
Topological Insulators ◽  
Second Order ◽  
Square Root

scholarly journals Dual-Polarization Second-Order Photonic Topological Insulators

2021 ◽  
Vol 15 (3) ◽  
Author(s):  
Yafeng Chen ◽  
Fei Meng ◽  
Zhihao Lan ◽  
Baohua Jia ◽  
Xiaodong Huang
Keyword(s):  
Topological Insulators ◽  
Second Order ◽  
Dual Polarization

scholarly journals A Second-Order Exact Ensemble Square Root Filter for Nonlinear Data Assimilation

2015 ◽  
Vol 143 (4) ◽  
pp. 1347-1367 ◽  
Author(s):  
Julian Tödter ◽  
Bodo Ahrens
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Second Order ◽  
Square Root ◽  
Computationally Efficient ◽  
Research Activities ◽  
Wide Range ◽  
Matrix Square Root ◽  
Non Gaussian ◽  
Ensemble Transform

Abstract The ensemble Kalman filter (EnKF) and its deterministic variants, mostly square root filters such as the ensemble transform Kalman filter (ETKF), represent a popular alternative to variational data assimilation schemes and are applied in a wide range of operational and research activities. Their forecast step employs an ensemble integration that fully respects the nonlinear nature of the analyzed system. In the analysis step, they implicitly assume the prior state and observation errors to be Gaussian. Consequently, in nonlinear systems, the analysis mean and covariance are biased, and these filters remain suboptimal. In contrast, the fully nonlinear, non-Gaussian particle filter (PF) only relies on Bayes’s theorem, which guarantees an exact asymptotic behavior, but because of the so-called curse of dimensionality it is exposed to weight collapse. Here, it is shown how to obtain a new analysis ensemble whose mean and covariance exactly match the Bayesian estimates. This is achieved by a deterministic matrix square root transformation of the forecast ensemble, and subsequently a suitable random rotation that significantly contributes to filter stability while preserving the required second-order statistics. The properties and performance of the proposed algorithm are further investigated via a set of experiments. They indicate that such a filter formulation can increase the analysis quality, even for relatively small ensemble sizes, compared to other ensemble filters in nonlinear, non-Gaussian scenarios. Localization enhances the potential applicability of this PF-inspired scheme in larger-dimensional systems. The proposed algorithm, which is fairly easy to implement and computationally efficient, is referred to as the nonlinear ensemble transform filter (NETF).

scholarly journals The square root problem for second-order, divergence form operators with mixed boundary conditions on L p

2014 ◽  
Vol 15 (1) ◽  
pp. 165-208 ◽  
Author(s):  
Pascal Auscher ◽  
Nadine Badr ◽  
Robert Haller-Dintelmann ◽  
Joachim Rehberg
Keyword(s):  
Boundary Conditions ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Divergence Form ◽  
Second Order ◽  
Square Root

scholarly journals Square-root non-Bloch topological insulators in non-Hermitian ring resonators

2021 ◽  
Author(s):  
Zekun Lin ◽  
Shaolin Ke ◽  
Xuefeng Zhu ◽  
Xun Li
Keyword(s):  
Topological Insulators ◽  
Ring Resonators ◽  
Square Root
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