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Ammonium-ion batteries are promising solutions for large-scale energy storage systems owing to their cost-effectiveness, safety, and sustainability. Herein, we propose an aqueous ammonium-ion battery based on an organic poly(1,5-naphthalenediamine) anode and an inorganic Prussian blue cathode in 19 ​M ​(M: mol kg−1) CH3COONH4 electrolyte. Its operation involves a reversible coordination reaction (C=N/C–N– conversion) in the anode and the NH4+ insertion/extraction reaction in the cathode, along with NH4+ acting as the charge carrier in a rocking-chair battery. Benefiting from the fast kinetics and stability of both electrodes, this aqueous ammonium-ion battery shows an excellent rate capability and long cycle stability for 500 cycles. Moreover, an energy density as high as 31.8 ​Wh kg−1 can be achieved, based on the total mass of the cathode and anode. Surprisingly, this aqueous ammonium-ion battery works well over a wide temperature range from −40 to 80 ​°C. This work will provide new opportunities to build wide-temperature aqueous batteries and broaden the horizons for large-scale energy storage systems.

Three small molecule organic compounds based on conjugated acetylene-linked methoxy triphenylamine terminal groups with different substituted thiophene cores were synthesized and firstly applied as hole-transporting materials (HTMs). The electron-deficient acetylene linkers can tune the energy levels of frontier molecular orbitals. The physical property measurements show that the HTMs (CJ-05, CJ-06, and CJ-07) possess good stability, hydrophobicity, and film-forming ability. Further, the HTMs were applied in the MAPbI3-based perovskite solar cells (PSCs), and the best power conversion efficiency (PCE) of 6.04%, 6.77%, and 6.48% was achieved, respectively, which implies that they exhibit great potential in photovoltaic applications.

Abstract By exploiting Toeplitz-like structure and non-Hermitian dense property of the discrete coefficient matrix, a new double-layer iterative method called SHSS-PCG method is employed to solve the linear systems originating from the implicit finite difference discretization of fractional diffusion equations (FDEs). The method is a combination of the single-step Hermitian and skew-Hermitian splitting (SHSS) method with the preconditioned conjugate gradient (PCG) method. Further, the new circulant preconditioners are proposed to improve the efficiency of SHSS-PCG method, and the computation cost is further reduced via using the fast Fourier transform (FFT). Theoretical analysis shows that the SHSS-PCG iterative method with circulant preconditioners is convergent. Numerical experiments are given to show that our SHSS-PCG method with circulant preconditioners preforms very well, and the proposed circulant preconditioners are very efficient in accelerating the convergence rate.

The Picard-HSS iterative method is proposed to solve the absolute value equation (AVE). To further improve its performance, a nonlinear HSS-like iterative method is proposed. Compared to that the Picard-HSS method is an innerouter double-layer iterative scheme, the proposed nonlinear HSS-like iteration is only a monolayer iterative method and the iteration vector could be updated timely. Some numerical experiments are used to demonstrate that the nonlinear HSSlike method is feasible, robust and effective. [ABSTRACT FROM AUTHOR]

By exploiting the special structure of the (1, 1)- block in the coefficient matrix of saddle point problems, a local circulant and residue splitting (LCRS) iterative method is proposed to solve Toeplitz-structured saddle point problems, and the splitting matrix serve as a preconditioner to accelerate the convergence rate of Krylov subspace method such as GMRES. The advantage of these methods are that the elapsed CPU time of each iteration is reduced considerably by using of the fast Fourier transform (FFT). The convergence theorem is established under suitable conditions. Numerical experiments of a model Stokes problem are presented to show that the LCRS is used as either solver or preconditioner to GMRES method often outperform other tested methods in the elapsed CPU time. [ABSTRACT FROM AUTHOR]

The spectral properties of a class of block 2x2 matrix are studied, which arise in the numercial solutions of PDE-constrained optimization problems. Based on the Schur complement approximate approach and inexact Uzawa preconditioner, the eigenvalues distribution of preconditioned matrix is discussed by the similarity transformation. Moreover, The numerical experiments originated in PDE-constrained optimization problem are presented to show that the theoretical bound of the eigenvalues is in good agreement with its practical bound. [ABSTRACT FROM AUTHOR]

The goal of this paper is to solve the complex symmetric linear systems generated from the discretization of the space fractional coupled nonlinear Schrödinger (CNLS) equations, whose coefficient matrix is equal to the sum of a symmetric positive definite Toeplitz matrix and a Hermitian positive definite complex diagonal matrix. In order to make the best use of the full Toeplitz structure of the coefficient matrix, a new Toeplitz and diagonal splitting (TDS) is given and the corresponding TDS iteration method is proposed to solve the discretized linear systems, then two circulant preconditioners based on Strang’s and T. Chan’s circulant approximation, are proposed to accelerate the convergence of the preconditioned conjugated gradient (PCG) method for solving the first linear sub-system in the TDS method. Theoretical analysis and numerical experiments demonstrate that the TDS method is unconditional convergence and the TDS-PCG inner-outer iteration method with two circulant preconditioners to solve the discretization linear systems of the space fractional CNLS equations is feasible and efficient. [ABSTRACT FROM AUTHOR]