RESUMO
Uniform error estimates with power-type asymptotic constants of the finite element method for the unsteady Navier−Stokes equations are deduced in this paper. By introducing an iterative scheme and studying its convergence, we firstly derive that the solution of the Navier−Stokes equations is bounded by power-type constants, where we avoid applying the Gronwall lemma, which generates exponential-type factors. Then, the technique is extended to the error estimate of the long-time finite element approximation. The analyses show that, under some assumptions on the given data, the asymptotic constants in the finite element error estimates for the unsteady Navier−Stokes equations are uniformly power functions with respect to the initial data, the viscosity, and the body force for all time t>0. Finally, some numerical examples are shown to verify the theoretical predictions.
RESUMO
Mixed tin-lead (Sn-Pb) perovskites have attracted the attention of the community due to their narrow bandgap, ideal for photovoltaic applications, especially tandem solar cells. However, the oxidation and rapid crystallization of Sn2+ and the interfacial traps hinder their development. Here, cross-linkable [6,6]-phenyl-C61-butyric styryl dendron ester (C-PCBSD) is introduced during the quenching step of perovskite thin film processing to suppress the generation of surface defects at the electron transport layer interface and improve the bulk crystallinity. The C-PCBSD has strong coordination ability with Sn2+ and Pb2+ perovskite precursors, which retards the crystallization process, suppresses the oxidation of Sn2+, and improves the perovskite bulk and surface crystallinity, yielding films with reduced nonradiative recombination and enhanced interface charge extraction. Besides, the C-PCBSD network deposited on the perovskite surface displays superior hydrophobicity and oxygen resistance. Consequently, the devices with C-PCBSD obtain PCEs of up to 23.4% and retained 97% of initial efficiency after 2000 h of storage in a N2 atmosphere.
RESUMO
Design of functionalized biomimetic scaffolds is one of the key approaches for regenerative medicine and other biomedical applications. Development of engineered tissue should optimize organization and function of cells and tissue in vitro as well as in vivo. Surface topography is one factor controlling cellular behavior and tissue development. By topographical patterning of biocompatible materials, highly functionalized scaffolds can be developed. Gelatin is hereby a promising candidate due to its biocompatibility and biodegradability. It is low in cost and easy to handle, enabling a variety of applications in science and medicine. However, for biomedical applications at physiological conditions, gelatin has to be additionally stabilized since its gel-sol-transition temperature lies beneath the human body temperature. This is realized by a reagent-free cross-linking technique utilizing electron beam treatment. By topographical patterning, gelatin can be functionalized toward scaffolds for cell cultivation and tissue development. Thereby, customized patterns are transferred onto gelatin hydrogels via molds. Thermal stabilization of gelatin is then achieved by electron-induced cross-linking. In this study, we investigate the influence of gelatin concentration and irradiation dose on pattern transfer, long-term stability of topographically patterned gelatin hydrogels, and their impact on the cellular behavior of human umbilical vein endothelial cells as well as normal human dermal fibroblasts. We will show that contact guidance occurs for both cell types due to a concrete stripe pattern. In addition, the presented studies show a high degree of cytocompatibility, indicating a high potential of topographically patterned gelatin hydrogels as tissue development scaffold for prospective biomedical applications.