In recent years, there has been a growing interest in analyzing and quantifying the effects of random inputs in the solution of ordinary/partial differential equations. To this end, the spectral ...stochastic finite element method (SSFEM) is the most popular method due to its fast convergence rate. Recently, the stochastic sparse grid collocation method has emerged as an attractive alternative to SSFEM. It approximates the solution in the stochastic space using Lagrange polynomial interpolation. The collocation method requires only repetitive calls to an existing deterministic solver, similar to the Monte Carlo method. However, both the SSFEM and current sparse grid collocation methods utilize global polynomials in the stochastic space. Thus when there are steep gradients or finite discontinuities in the stochastic space, these methods converge very slowly or even fail to converge. In this paper, we develop an adaptive sparse grid collocation strategy using piecewise multi-linear hierarchical basis functions. Hierarchical surplus is used as an error indicator to automatically detect the discontinuity region in the stochastic space and adaptively refine the collocation points in this region. Numerical examples, especially for problems related to long-term integration and stochastic discontinuity, are presented. Comparisons with Monte Carlo and multi-element based random domain decomposition methods are also given to show the efficiency and accuracy of the proposed method.
Solid‐state materials with efficient room‐temperature phosphorescence (RTP) emissions have found widespread applications in materials science, while liquid or solution‐phase pure organic RTP emission ...systems has been rarely reported, because of the nonradiative decay and quenchers from the liquid medium. Reported here is the first example of visible‐light‐excited pure organic RTP in aqueous solution by using a supramolecular host‐guest assembly strategy. The unique cucurbit8uril‐mediated quaternary stacking structure allows tunable photoluminescence and visible‐light excitation, enabling the fabrication of multicolor hydrogels and cell imaging. The present assembly‐induced emission approach, as a proof of concept, contributes to the construction of novel metal‐free RTP systems with tunable photoluminescence in aqueous solution, providing broad opportunities for further applications in biological imaging, detection, optical sensors, and so forth.
True colors: An assembly‐induced emission strategy was utilized to endow a simple dye molecule with room‐temperature phosphorescence and tunable photoluminescence in aqueous solution. The obtained supramolecular assembly structure has intriguing photophysical properties and enables the fabrication of multicolor hydrogels and cell imaging.
A computational methodology is developed to address the solution of high-dimensional stochastic problems. It utilizes high-dimensional model representation (HDMR) technique in the stochastic space to ...represent the model output as a finite hierarchical correlated function expansion in terms of the stochastic inputs starting from lower-order to higher-order component functions. HDMR is efficient at capturing the high-dimensional input–output relationship such that the behavior for many physical systems can be modeled to good accuracy only by the first few lower-order terms. An adaptive version of HDMR is also developed to automatically detect the important dimensions and construct higher-order terms using only the important dimensions. The newly developed adaptive sparse grid collocation (ASGC) method is incorporated into HDMR to solve the resulting sub-problems. By integrating HDMR and ASGC, it is computationally possible to construct a low-dimensional stochastic reduced-order model of the high-dimensional stochastic problem and easily perform various statistic analysis on the output. Several numerical examples involving elementary mathematical functions and fluid mechanics problems are considered to illustrate the proposed method. The cases examined show that the method provides accurate results for stochastic dimensionality as high as 500 even with large-input variability. The efficiency of the proposed method is examined by comparing with Monte Carlo (MC) simulation.
The development of precious‐metal alternative electrocatalysts for oxygen reduction reaction (ORR) is highly desired for a variety of fuel cells, and single atom catalysts (SACs) have been envisaged ...to be the promising choice. However, there remains challenges in the synthesis of high metal loading SACs (>5 wt.%), thus limiting their electrocatalytic performance. Herein, a facile self‐sacrificing template strategy is developed for fabricating Co single atoms along with Co atomic clusters co‐anchored on porous‐rich nitrogen‐doped graphene (Co SAs/AC@NG), which is implemented by the pyrolysis of dicyandiamide with the formation of layered g‐C3N4 as sacrificed templates, providing rich anchoring sites to achieve high Co loading up to 14.0 wt.% in Co SAs/AC@NG. Experiments combined with density functional theory calculations reveal that the co‐existence of Co single atoms and clusters with underlying nitrogen doped carbon in the optimized Co40SAs/AC@NG synergistically contributes to the enhanced electrocatalysis for ORR, which outperforms the state‐of‐the‐art Pt/C catalysts with presenting a high half‐wave potential (E1/2 = 0.890 V) and robust long‐term stability. Moreover, the Co40SAs/AC@NG presents excellent performance in Zn–air battery with a high‐peak power density (221 mW cm−2) and strong cycling stability, demonstrating great potential for energy storage applications.
High‐loading Co single atoms and Co atomic clusters co‐anchored on porous‐rich nitrogen‐doped graphene (Co SAs/AC@NG) is constructed via a facile self‐sacrificing template strategy. The Co40SAs/AC@NG catalyst demonstrates remarkable performance with a half‐wave potential of 0.890 V for oxygen reduction reaction and a large power density of 221 mW cm−2 toward Zn–air battery.
So far, pure organic room temperature phosphorescence (RTP) materials are developing rapidly and have become a research hotspot in the scientific community. They are regarded as valuable resources ...with great potential for development in many fields, such as biomedicine, information multi‐level encryption, smart anti‐counterfeiting, and so on. Among them, a series of pure organic RTP polymer systems emerged at the right moment based on the excellent properties of polymers such as easy processing, low cost, and good biocompatibility. Furthermore, the huge molecular weight, long‐chain intertwined structure, and potential interactions with phosphors of polymers make them a focus for RTP emission. Herein, we describe the development history of this system in detail, explore the necessary factors for highly efficient emission from the phosphorescence emission process, and based on the dual effects of enhancing phosphorescence emission and shortening luminescence lifetime brought by heavy atoms, we summarize the internal mechanism and achievements of various researches from the perspective of heavy atom–containing and non‐heavy atom systems.
Pure organic room temperature phosphorescent polymers are divided into two categories. Phosphorescent dyes can be attached to the polymer chains by covalent bonds or blended with the polymers. The rigid network of polymers can suppress the nonradiative deactivation of triplet. Recent progress on organic room temperature phosphorescent polymers is comprehensively reviewed.
Production of hydrogen by electrochemical water splitting has been hindered by the high cost of precious metal catalysts, such as Pt, for the hydrogen evolution reaction (HER). In this work, novel ...hierarchical β‐Mo2C nanotubes constructed from porous nanosheets have been fabricated and investigated as a high‐performance and low‐cost electrocatalyst for HER. An unusual template‐engaged strategy has been utilized to controllably synthesize Mo‐polydopamine nanotubes, which are further converted into hierarchical β‐Mo2C nanotubes by direct carburization at high temperature. Benefitting from several structural advantages including ultrafine primary nanocrystallites, large exposed surface, fast charge transfer, and unique tubular structure, the as‐prepared hierarchical β‐Mo2C nanotubes exhibit excellent electrocatalytic performance for HER with small overpotential in both acidic and basic conditions, as well as remarkable stability.
From the same sheet: Hierarchical β‐Mo2C nanotubes constructed of ultrathin nanosheets are designed and synthesized. Benefitting from ultra‐small primary nanocrystallites, a large exposed surface, fast charge transfer, and unique tubular structure, the as‐prepared hierarchical β‐Mo2C nanotubes exhibit excellent electrocatalytic performance for the hydrogen evolution reaction.
Pure organic, heavy‐atom‐free room‐temperature phosphorescence (RTP) materials have attracted much attention and have potential applications in photoelectric and biochemical material fields owing to ...their rich excited state properties. They offer long luminescent lifetime, diversified design, and facile preparation. However, recent achievements of efficient phosphorescence under ambient conditions mainly focus on ordered crystal lattices or embedding into rigid matrices, which require strict growth conditions and have poor reproducibility. Herein, we developed a concise approach to give RTP with a decent quantum yield and ultralong phosphorescence lifetime in the amorphous state by radical binary copolymerization of acrylamide and different phosphors with oxygen‐containing functional groups. The cross‐linked hydrogen‐bonding networks between the polymeric chains immobilize phosphors to suppress non‐radiative transitions and provide a microenvironment to shield quenchers.
He ain't heavy: The radical binary copolymerization of acrylamide and different phosphors with oxygen‐containing functional groups allows efficient room‐temperature phosphorescence with ultralong lifetime in an amorphous polymer. The cross‐linked hydrogen‐bonding networks between the polymeric chains immobilize phosphors and suppress non‐radiative transitions.
Among the many novel photocatalytic systems developed in very recent years, plasmonic photocatalytic composites possess great potential for use in applications and are one of the most intensively ...investigated photocatalytic systems owing to their high solar energy utilization efficiency. In these composites, the plasmonic nanoparticles (PNPs) efficiently absorb solar light through localized surface plasmon resonance and convert it into energetic electrons and holes in the nearby semiconductor. This energy transfer from PNPs to semiconductors plays a decisive role in the overall photocatalytic performance. Thus, the underlying physical mechanism is of great scientific and technological importance and is one of the hottest topics in the area of plasmonic photocatalysts. In this review, we examine the very recent advances in understanding the energy transfer process in plasmonic photocatalytic composites, describing both the theoretical basis of this process and experimental demonstrations. The factors that affect the energy transfer efficiencies and how to improve the efficiencies to yield better photocatalytic performance are also discussed. Furthermore, comparisons are made between the various energy transfer processes, emphasizing their limitations/benefits for efficient operation of plasmonic photocatalysts.
► KPCA is used to construct a reduced order stochastic model of permeability. ► A new approach is proposed to solve the pre-image problem in KPCA. ► Polynomial chaos is used to provide a parametric ...stochastic input model. ► Flow in porous media with channelized permeability is considered.
Stochastic analysis of random heterogeneous media provides useful information only if realistic input models of the material property variations are used. These input models are often constructed from a set of experimental samples of the underlying random field. To this end, the Karhunen–Loève (K–L) expansion, also known as principal component analysis (PCA), is the most popular model reduction method due to its uniform mean-square convergence. However, it only projects the samples onto an optimal linear subspace, which results in an unreasonable representation of the original data if they are non-linearly related to each other. In other words, it only preserves the first-order (mean) and second-order statistics (covariance) of a random field, which is insufficient for reproducing complex structures. This paper applies kernel principal component analysis (KPCA) to construct a reduced-order stochastic input model for the material property variation in heterogeneous media. KPCA can be considered as a nonlinear version of PCA. Through use of kernel functions, KPCA further enables the preservation of higher-order statistics of the random field, instead of just two-point statistics as in the standard Karhunen–Loève (K–L) expansion. Thus, this method can model non-Gaussian, non-stationary random fields. In this work, we also propose a new approach to solve the pre-image problem involved in KPCA. In addition, polynomial chaos (PC) expansion is used to represent the random coefficients in KPCA which provides a parametric stochastic input model. Thus, realizations, which are statistically consistent with the experimental data, can be generated in an efficient way. We showcase the methodology by constructing a low-dimensional stochastic input model to represent channelized permeability in porous media.
Exploring highly active and cost‐efficient single‐atom catalysts (SACs) for oxygen reduction reaction (ORR) is critical for the large‐scale application of Zn–air battery. Herein, density functional ...theory (DFT) calculations predict that the intrinsic ORR activity of the active metal of SACs follows the trend of Co > Fe > Ni ≈ Cu, in which Co SACs possess the best ORR activity due to its optimized spin density. Guided by DFT calculations, four kinds of transition metal single atoms embedded in 3D porous nitrogen‐doped carbon nanosheets (MSAs@PNCN, M = Co, Ni, Fe, Cu) are synthesized via a facile NaCl‐template assisted strategy. The resulting MSAs@PNCN displays ORR activity trend in lines with the theoretical predictions, and the Co SAs@PNCN exhibits the best ORR activity (E1/2 = 0.851 V), being comparable to that of Pt/C under alkaline conditions. X‐ray absorption fine structure (XAFS) spectra verify the atomically dispersed Co‐N4 sites are the catalytically active sites. The highly active CoN4 sites and the unique 3D porous structure contribute to the outstanding ORR performance of Co SAs@PNCN. Furthermore, the Co SAs@PNCN catalyst is employed as cathode in Zn–air battery, which can deliver a large power density of 220 mW cm–2 and maintain robust cycling stability over 530 cycles.
Four kinds of transition metal single atoms embedded in 3D porous nitrogen‐doped carbon nanosheets (MSAs@PNCN, M = Co, Ni, Fe, Cu) are constructed via a facile NaCl‐template assisted strategy. The Co SAs@PNCN catalysts demonstrate remarkable performance with a half‐wave potential of 0.851 V for oxygen reduction reaction and a large power density of 220 mW cm–2 toward Zn–air battery.
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