Dion-Jacobson-Phase 2D Sn-Based Perovskite Comprising a High Dipole Moment of π-Conjugated Short-Chain Organic Spacers for High-Performance Solar Cell Applications.

The stability issue of Sn-based perovskite solar cells (PSCs) is expected to be resolved by involving a two-dimensional (2D) layered structure. However, Sn-based 2D PSCs, especially Dion-Jacobson (DJ)-phase ones with potentially good stability, have rarely been reported. Herein, superior DJ-phase Sn 2D perovskites with 3-aminobenzylamine (3ABA2+) or 4-aminobenzylamine (4ABA2+) π-conjugated short-chain ligands are reported to fabricate efficient 2D lead-free PSCs. Notably, the high dipole moment of the 3ABAI2 organic spacer is approved to possess faster charge transfer for forming (3ABA)FA4Sn5I16 2D perovskite with an extremely low exciton binding energy (only 84 meV). In combination with a diacetate partial substitution and methylamine iodide/bromide (MAI/MABr) post-treatment strategy to delay crystallization and improve compactness and coverage of the perovskite film, a record power conversion efficiency (PCE) of 6.81% and stability of 840 h (less than 5% degradation in a N2 atmosphere for unencapsulated devices) are acquired in eventual (3ABA)FA4Sn5I16 2D PSCs, which are among the highest PCE and the longest stability of Sn-based 2D PSCs reported to date. Our work provides a prospective molecule design and film preparation strategy of 2D Sn perovskites toward nontoxic high-performance tin-based PSCs, which pushes the almost stagnant research forward.

Almost Surely Exponential Convergence Analysis of Time Delayed Uncertain Cellular Neural Networks Driven by Liu Process via Lyapunov-Krasovskii Functional Approach.

As with probability theory, uncertainty theory has been developed, in recent years, to portray indeterminacy phenomena in various application scenarios. We are concerned, in this paper, with the convergence property of state trajectories to equilibrium states (or fixed points) of time delayed uncertain cellular neural networks driven by the Liu process. By applying the classical Banach's fixed-point theorem, we prove, under certain conditions, that the delayed uncertain cellular neural networks, concerned in this paper, have unique equilibrium states (or fixed points). By carefully designing a certain Lyapunov-Krasovskii functional, we provide a convergence criterion, for state trajectories of our concerned uncertain cellular neural networks, based on our developed Lyapunov-Krasovskii functional. We demonstrate under our proposed convergence criterion that the existing equilibrium states (or fixed points) are exponentially stable almost surely, or equivalently that state trajectories converge exponentially to equilibrium states (or fixed points) almost surely. We also provide an example to illustrate graphically and numerically that our theoretical results are all valid. There seem to be rare results concerning the stability of equilibrium states (or fixed points) of neural networks driven by uncertain processes, and our study in this paper would provide some new research clues in this direction. The conservatism of the main criterion obtained in this paper is reduced by introducing quite general positive definite matrices in our designed Lyapunov-Krasovskii functional.

Global Existence and Fixed-Time Synchronization of a Hyperchaotic Financial System Governed by Semi-Linear Parabolic Partial Differential Equations Equipped with the Homogeneous Neumann Boundary Condition.

Chaotic nonlinear dynamical systems, in which the generated time series exhibit high entropy values, have been extensively used and play essential roles in tracking accurately the complex fluctuations of the real-world financial markets. We are concerned with a system of semi-linear parabolic partial differential equations supplemented by the homogeneous Neumann boundary condition, which governs a financial system comprising the labor force, the stock, the money, and the production sub-blocks distributed in a certain line segment or planar region. The system derived by removing the terms involved with partial derivatives with respect to space variables from our concerned system was demonstrated to be hyperchaotic. We firstly prove, via Galerkin's method and establishing a priori inequalities, that the initial-boundary value problem for the concerned partial differential equations is globally well posed in Hadamard's sense. Secondly, we design controls for the response system to our concerned financial system, prove under some additional conditions that our concerned system and its controlled response system achieve drive-response fixed-time synchronization, and provide an estimate on the settling time. Several modified energy functionals (i.e., Lyapunov functionals) are constructed to demonstrate the global well-posedness and the fixed-time synchronizability. Finally, we perform several numerical simulations to validate our synchronization theoretical results.