On the application of wavelet transform to the solution of integral equations for acoustic radiation and scattering

The application of wavelets is explored to solve acoustic radiation and scattering problems. A new wavelet approach is presented for solving two-dimensional and axisymmetric acoustic problems. It is different from the previous methods in which Galerkin formulation or wavelet matrix transform approach is used. The boundary quantities are expended in terms of a basis of the periodic, orthogonal wavelets on the interval. Using wavelet transform leads a highly sparse matrix system. It can avoid an additional integration in Galerkin formulation, which may be very computationally expensive. The techniques of the singular integrals in two-dimensional and axisymmetric wavelet formulation are proposed. The new method can solve the boundary value problems with Dirichlet, Neumann and mixed conditions and treat axisymmetric bodies with arbitrary boundary conditions. It can be suitable for the solution at large wave numbers. A series of numerical examples are given. The comparisons of the results from new approach with those from boundary element method and analytical solutions demonstrate that the new techique has a fast convergence and high accuracy.

Anomalous self-optimization of sulfate ions for boosted oxygen evolution reaction

Broadly,the oxygen evolution reaction(OER)has been deeply understood as a significant part of energy conversion and storage.Nevertheless,the anions in the OER catalysts have been neglected for various reasons such as inactive sites,dissolution,and oxidation,amongst others.Herein,we applied a model catalyst s-Ni(OH)2 to track the anionic behavior in the catalyst during the electrochemical process to fill this gap.The advanced operando synchrotron radiation Fourier transform infrared(SR-FTIR)spectroscopy,synchrotron radiation photoelectron spectroscopy(SRPES)depth detection and differential X-ray absorption fine structure(D-XAFS)spectrum jointly point out that some oxidized sulfur species(SO_(4)^(2-))will selfoptimize new Ni–S bonds during OER process.Such amazing anionic self-optimization(ASO)behavior has never been observed in the OER process.Subsequently,the optimization-derived component shows a significantly improved electrocatalytic performance(activity,stability,etc.)compared to reference catalyst Ni(OH)_(2).Theoretical calculation further suggests that the ASO process indeed derives a thermodynamically stable structure of the OER catalyst,and then gives its superb catalytic performance by optimizing the thermodynamic and kinetic processes in the OER,respectively.This work demonstrates the vital role of anions in the electrochemical process,which will open up new perspectives for understanding OER and provide some new ideas in related fields(especially catalysis and chemistry).