Low rank approximation method for perturbed linear systems with applications to elliptic type stochastic PDEs

In this paper, we propose a low rank approximation method for efficiently solving stochastic partial differential equations. Specifically, our method utilizes a novel low rank approximation of the stiffness matrices, which can significantly reduce the computational load and storage requirements associated with matrix inversion without losing accuracy. To demonstrate the versatility and applicability of our method, we apply it to address two crucial uncertainty quantification problems: stochastic elliptic equations and optimal control problems governed by stochastic elliptic PDE constraints. Based on varying dimension reduction ratios, our algorithm exhibits the capability to yield a high precision numerical solution for stochastic partial differential equations, or provides a rough representation of the exact solutions as a pre-processing phase. Meanwhile, our algorithm for solving stochastic optimal control problems allows a diverse range of gradient-based unconstrained optimization methods, rendering it particularly appealing for computationally intensive large-scale problems. Numerical experiments are conducted and the results provide strong validation of the feasibility and effectiveness of our algorithm

Anomalous Floquet non-Hermitian skin effect in a ring resonator lattice

We present a one-dimensional coupled ring resonator lattice exhibiting a variant of the non- Hermitian skin effect (NHSE) that we call the anomalous Floquet NHSE. Unlike existing approaches to achieving the NHSE by engineering gain and loss on different ring segments, our design uses fixed on-site gain or loss in each ring. The anomalous Floquet NHSE is marked by the existence of skin modes at every value of the Floquet quasienergy, allowing for broadband asymmetric transmission. Varying the gain/loss induces a non-Hermitian topological phase transition, reversing the localization direction of the skin modes. An experimental implementation in an acoustic lattice yields good agreement with theoretical predictions, with a very broad relative bandwidth of around 40%.Comment: 7 pages, 3 figure

Impossible Differential Cryptanalysis of FOX

Block ciphers are the very foundation of computer and information security. FOX, also known as IDEA NXT, is a family of block ciphers published in 2004 and is famous for its provable security to cryptanalysis. In this paper, we apply impossible differential cryptanalysis on FOX cipher. We find a 4-round impossible difference, by using which adversaries can attack 5, 6 and 7-round FOX64 with $2^{71}$, $2^{135}$ and $2^{199}$ one-round encryptions respectively. Compared to the previous best attack with $2^{109.4}$, $2^{173.4}$ and $2^{237.4}$ full-round encryptions to 5, 6 and 7-round FOX64, the method in this paper is the best attack to FOX cipher. This attack can also be applied to 5-round FOX128 with $2^{135}$ one-round encryptions

Hexagonal Boron Nitride Thick Film Grown on a Sapphire Substrate via Low-Pressure Chemical Vapor Deposition

Hexagonal boron nitride (h-BN) with a certain thickness has wide applications in semiconductor electronic devices. In this study, the relationship between the amount of ammonia borane and the thickness of h-BN films was investigated via low-pressure chemical vapor deposition (LPCVD) on a noncatalytic c-plane Al2O3 substrate. Through various characterization methods, the grown film was confirmed to be h-BN. The effect of the precursor mass on the growth thickness of the h-BN film was studied, and it was found that the precursor mass significantly affected the growth rate of the h-BN film. The results from SEM show that the amount of ammonia borane is 2000 mg and a 1.295-μm h-BN film is obtained. It will provide an experimental reference for the growth of thicker h-BN materials to prepare high-efficiency neutron detectors for radiation detection

An investigation of formaldehyde concentration in residences and the development of a model for the prediction of its emission rates

Indoor air pollution caused by formaldehyde associated with building materials imposes a variety of acute and chronic adverse effects on people’s health. The aim of this research is to investigate the concentrations of formaldehyde in residences and develop emission rate prediction model in residential buildings. On-site measurements including the indoor and outdoor concentrations of formaldehyde and CO2 were carried out in 42 urban residences in Chongqing. The people occupancy schedule in different functional rooms was obtained by observing the change in CO2 concentration. A robust model for the estimation of formaldehyde emission rates using CO2 as the tracer gas; associated with a Monte-Carlo simulation of occupant activities and the characteristics of residences; has been developed. It is revealed that the mean indoor formaldehyde concentration was 30.12μg/m3, which was slightly higher than the outdoor concentration of 27.80μg/m3. The emission rates of 61.82±52.39 and 49.69±42.13µg/h/m2 (mean±SD) during the daytime and nighttime, respectively with a daily average of 57.20±48.79µg/h/m2. The significant contribution to indoor formaldehyde concentration was from indoor sources. Indoor formaldehyde source control is suggested to be an efficient way to control the indoor concentration