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Organic-inorganic halide perovskites have emerged as excellent candidates for low-cost photovoltaics and optoelectronics. While the predominant recent trend in designing perovskites for efficient and stable solar cells has been to mix different A-site cations, the role of A-site cations is still limited to tune the lattice and bandgap of perovskites. Herein we compare the optoelectronic properties of acetamidinum (Ace) and guanidinium (Gua) mixed methylammonium lead iodide perovskites and shed a light on the hidden role of A-site cation on the carrier mobility of mixed-cation lead iodide perovskites. The cations do not affect the bandgap of the perovskites since the orbitals from Ace and Gua do not contribute to the band edges of the material. However, the mobility of the Ace mixed perovskite is significantly enhanced to be an order of magnitude higher than that of the pristine perovskite. We apply the Ace mixed perovskite in hole-conductor-free printable mesoscopic perovskite solar cells and obtain a stabilized PCE of over 18% (certified 17.7%), which is the highest certified efficiency so far.

In this paper, we present a Petrov–Galerkin finite element method for a class of chemotaxis models defined on surfaces, which describe the movement by one community in reaction to one chemical or biological signal on manifolds. It is desired for numerical methods to satisfy discrete maximum principle and discrete mass conservation property, which is a challenge due to the singular behavior of numerical solution. Thus a Petrov–Galerkin method is combined with an effective mass conservation factor to overcome the challenge. Furthermore, we prove two facts, this method maintains positivity and discrete mass conservation property. In addition, decoupled approach is applied based on the gradient and Laplacian recoveries to solve the coupling system. The relevant stability analyses is provided. Finally, numerical simulations of blowing-up problems and pattern formulations demonstrate the effectiveness of the proposed method.

The reaction–diffusion equations models on surfaces have received growing interest and have been applied to simulate the physical processes and chemical reactions on ultra-thin materials, solid surfaces and biological films. In this article, we present a lifted local Galerkin method for solving the reaction–diffusion equations on implicit surfaces. The basic idea of proposed method is to discretize the equations on tangent plane of each surface node. Based on this idea, for each surface node, we first construct the local triangulation mesh via using this node and lifted points of its neighborhood on the tangent plane for this node. After setting a constant extension of surface data between each neighborhood and lifted point, we construct the discrete scheme by a local Galerkin method. Finally, the convergence tests and some applications in engineering science of the proposed method are shown to verify the feasibility and correction.

The lumped mass method is extended to the surface finite element method for solving the surface parabolic equations. The main purpose of the proposed method is to overcome the difficulty that the surface finite element method does not guarantee the maximal principle of the surface heat equation. Optimal error estimates are given for the semi-discrete and fully-discrete schemes of the proposed method respectively. The maximum principle is shown for surface heat equations and its preservation by the lumped mass surface finite element under the Delaunay type triangulation. Moreover, some results of positivity and monotonicity are derived for nonlinear parabolic equations. Finally some numerical experiments are displayed to illustrate the validity and numerical performance of the proposed method.

In this article, we develop a fully decoupled, linear and positivity-preserving finite element scheme for solving the chemotaxis–Stokes equations, which describe the biological chemotaxis phenomenon in the fluid environment. To deal with the strong coupling of the problem, we first consider a fully decoupled and linear semi-discrete scheme, in which we only need to solve several linearized sub-problems at each time step for the velocity, pressure, oxygen concentration and cell density, respectively. Then, based on the linear finite element method for the spatial discretization , the flux-corrected transport algorithm is extended to the oxygen concentration and cell density sub-problems to preserve their positivity. Finally, we show a series of numerical examples to verify its efficiency. We also find that better simulation can be obtained by regularizing the cut-off function and setting a random initial cell density in the equations.

Impurity accumulation, which decreases the accuracy of flow measurement, is a critical problem when applying Z-shaped or U-shaped ultrasonic flow meters on straight PFA tubes. It can be expected that the guided wave can be used to implement flow measurement on straight PFA tubes. In this paper, the propagation of guided wave is explained by finite element simulations for the flow meter design. Conditions of guided wave generation, including the excitation frequency and the wedge structure, are studied in the simulations. The wedge is designed as a cone which is friendly to be manufactured and installed. The cone angle, the piezoelectric wafer’s resonant frequency and the vibration directions are studied in the simulations. The simulations shows that the propagation of guided wave in thin PFA tubes is influenced by the piezoelectric wafers’ resonant frequency and the vibration direction when the mode is on the ‘water line’. Based on the results of the simulations, an experiment is conducted to verify the principles of excitation conditions, which performs flow measurement on a straight PFA tube well.

We present numerical simulations for the surface Cahn–Hilliard equation which describes phase separation phenomenon occurred on general surfaces. The spatial discretization is based on surface finite element method while the temporal discretization methods are first- and second-order stabilized semi-implicit schemes which guarantee the free energy decay. An efficient and parameter-free adaptive time-stepping strategy is proposed based on the numerical energy stability generated by stabilized semi-implicit scheme. The main idea is to use discrete chemical potential, the byproduct of stabilized semi-implicit scheme, to estimate the variation of numerical energy that is used as a indicator to update the time step, the operation avoid calculating numerical energy with Gauss integral in each time step and reduce the calculated cost. In addition, optimal error estimate of first-order stabilized semi-implicit scheme in the case of curved surface are provided. Finally, numerical experiments are presented to demonstrate the stability, accuracy and efficiency of the proposed algorithms.

In this paper, a positivity preserving characteristic finite element method is presented to solve the transport and convection–diffusion–reaction equations on general surfaces. The surface finite element method, which solves a variation problem by the linear finite element space on a piecewise triangulated surface, is applied to spatial discretization. For the backtracking in characteristic derivative discretization, unlike the cases on the two-dimensional plane, the foots of approximate characteristics may locate in the outer domain of the surface. To determine the values of solution at the foots of characteristics, a new strategy, which permits larger time steps, is designed instead of the discrete closest point mapping method which has a strict time step restriction. By combining with the mass lumping technique, the proposed numerical scheme is positivity preserving. The proposed method can also be extended to the problems with nonlinear convection terms. Various numerical examples are performed to demonstrate the validity and accuracy of the proposed method.