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1.
本文研究了数值求解非自治随机微分方程的正则Euler-Maruyama分裂(CEMS)方法,该方程的漂移项系数带有刚性且允许超线性增长,扩散项系数满足全局Lipschitz条件.首先,证明了CEMS方法的强收敛性及收敛速度.其次,证明了在适当条件下CEMS方法是均方稳定的.进一步,利用离散半鞅收敛定理,研究了CEMS方法的几乎必然指数稳定性.结果表明,CEMS方法在漂移系数的刚性部分满足单边Lipschitz条件下可保持几乎必然指数稳定性.最后通过数值实验,检验了CEMS方法的有效性并证实了我们的理论结果.  相似文献   
2.
Controllable tailoring of metal-free/carbon-based nanostructures tends an encouraging way to enhance the bifunctional activity of electrodes, but a great challenge owing to the sluggish kinetics of oxygen evolution reaction (OER) and hydrogen evolution reaction (HER). Herein, a facile tempted-defects assisted fractionation strategy is presented to synthesize N, S, and O tri-doped metal-free catalyst (DE-TDAP). Due to this effective tempted-defects and heteroatoms interlinking in DE-TDAP, it delivers the lowest overpotential toward both the OER (346 mV) and HER (154 mV) at 10 mA cm?2. Remarkably, the DE-TDAP-electrode carries only a cell voltage of 1.81 V at 10 mA cm?2 for overall water splitting and long-term stability. Considerably, the density functional theory (DFT) calculation exposes that the tailored-defects in tri-doped interlinking could enhance bifunctional catalytic performance devising from lower Gibbs free energy of OER/HER intermediates on active sites. This struggle henceforth provides a perceptive understanding of the synergetic principles of heteroatom-interlinking-tailoring nanostructures in water splitting.  相似文献   
3.
Erosion and sediments transport processes have a great impact on industrial structures and on water quality. Despite its limitations, the Saint‐Venant‐Exner system is still (and for sure for some years) widely used in industrial codes to model the bedload sediment transport. In practice, its numerical resolution is mostly handled by a splitting technique that allows a weak coupling between hydraulic and morphodynamic distinct softwares but may suffer from important stability issues. In recent works, many authors proposed alternative methods based on a strong coupling that cure this problem but are not so trivial to implement in an industrial context. In this work, we then pursue 2 objectives. First, we propose a very simple scheme based on an approximate Riemann solver, respecting the strong coupling framework, and we demonstrate its stability and accuracy through a number of numerical test cases. However, second, we reinterpret our scheme as a splitting technique and we extend the purpose to propose what should be the minimal coupling that ensures the stability of the global numerical process in industrial codes, at least, when dealing with collocated finite volume method. The resulting splitting method is, up to our knowledge, the only one for which stability properties are fully demonstrated.  相似文献   
4.
In this paper, we study the local linear convergence properties of a versatile class of Primal–Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of the problem are partly smooth relative to smooth manifolds, we present a unified local convergence analysis framework for these methods. More precisely, in our framework, we first show that (i) the sequences generated by Primal–Dual splitting methods identify a pair of primal and dual smooth manifolds in a finite number of iterations, and then (ii) enter a local linear convergence regime, which is characterized based on the structure of the underlying active smooth manifolds. We also show how our results for Primal–Dual splitting can be specialized to cover existing ones on Forward–Backward splitting and Douglas–Rachford splitting/ADMM (alternating direction methods of multipliers). Moreover, based on these obtained local convergence analysis result, several practical acceleration techniques are discussed. To exemplify the usefulness of the obtained result, we consider several concrete numerical experiments arising from fields including signal/image processing, inverse problems and machine learning. The demonstration not only verifies the local linear convergence behaviour of Primal–Dual splitting methods, but also the insights on how to accelerate them in practice.  相似文献   
5.
In this paper we prove a shadowing lemma for pseudo orbits made by quasi-hyperbolic strings. We allow singularities in question and hence, in particular, the quasi-hyperbolic strings are formulated by the rescaled linear Poincaré flow instead of the usual linear Poincaré flow. We also introduce the sectional Poincaré map and rescaled sectional Poincaré map for Lipschitz vector fields on Banach spaces in the article.  相似文献   
6.
Bimetallic AgPd nanoparticles have been synthesized before, but the interfacial electronic effects of AgPd on the photocatalytic performance have been investigated less. In this work, the results of hydrogen evolution suggest that the bimetallic AgPd/g-C3N4 sample has superior activity to Ag/g-C3N4 and Pd/g-C3N4 photocatalysts. The UV/Vis diffuse reflectance spectroscopy, X-ray photoelectron spectroscopy, CO adsorption diffuse reflectance FTIR spectroscopy, and FTIR results demonstrate that in the AgPd/g-C3N4, the surface electronic structures of Pd and Ag are changed, which is beneficial for faster photogenerated electron transfer and greater H2O molecule adsorption. In situ ESR spectra suggest that, under visible light irradiation, there is more H2O dissociation to radical species on the AgPd/g-C3N4 photocatalyst. Furthermore, DFT calculations confirm the interfacial electronic effects of AgPd/g-C3N4, that is, Pdδ−⋅⋅⋅Agδ+, and the activation energy of H2O molecule dissociation on AgPd/g-C3N4 is the lowest, which is the main contributor to the enhanced photocatalytic H2 evolution.  相似文献   
7.
Photodeposition has been widely used as a mild and efficient synthetic method to deposit co‐catalysts. It is also worth studying how to synthesize non‐noble metal photocatalysts with uniform dispersion. Different synthetic conditions in photodeposition have a certain influence on particle size distribution and photocatalytic activity. Therefore, we designed experiments to prepare the inexpensive composite photocatalyst Ni(OH)2/g‐C3N4 by photodeposition. The Ni(OH)2 co‐catalysts disperse uniformly with particle sizes of about 10 nm. The photocatalytic hydrogen production rate of Ni(OH)2/g‐C3N4 reached about 19 mmol g?1 h?1, with the Ni(OH)2 deposition amount about 1.57 %. During 16 h stability testing, the rate of hydrogen production did not decrease significantly. The composite catalyst also revealed a good hydrogen production performance under sunlight. The Ni(OH)2 co‐catalyst enhanced the separation ability of photogenerated carriers, which was proved by surface photovoltage and fluorescence analysis.  相似文献   
8.
One of the most spectacular yet unsolved problems for the ICN -band photodissociation is the non-statistical spin-rotation F1 = N + 1/2 and F2 = N − 1/2 populations for each rotation level N of the CN fragment. The F1/F2 population difference function f(N) exhibits strong N and λ dependences with an oscillatory behavior. Such details were found to critically depend on the number of open-channel product states, namely, whether both I (2P3/2) and I (2P1/2) are energetically available or not as the dissociation partner. First, in the asymptotic region, the exchange and dipole-quadrupole inter-fragment interactions were studied in detail. Then, as the diabatic basis, we took the appropriate symmetry adapted products of the electronic and rotational wavefunctions for the F1 and F2 levels at the dissociation limits. We found that the adiabatic Hamiltonian exhibits Rosen–Zener–Demkov type nonadiabatic transitions reflecting the switch between the exchange interaction and the small but finite spin-rotation interaction within CN at the asymptotic region. This non-crossing type nonadiabatic transition occurs with the probability 1/2, that is, at the diabatic limit through a sudden switch of the quantization axis for CN spin S from the dissociation axis to the CN rotation axis N . We have derived semiclassical formulae for f(N) and the orientation parameters with a two-state model including the 3A′ and 4A′ electronic states, and with a four-state model including the 3A′ through 6A′ electronic states. These two kinds of interfering models explain general features of the F1 and F2 level populations observed by Zare's group and Hall's group, respectively. © 2018 Wiley Periodicals, Inc.  相似文献   
9.
With the ever‐increasing concerns on environmental pollution and energy crisis, it is of great urgency to develop high‐performance photocatalyst to eliminate organic pollutants from wastewater and produce hydrogen via water splitting. Herein, a polypyridyl‐based mixed covalent CuI/II complex with triangular {Cu3} and rhombic {Cu2Cl4} subunits alternately extended by mixed SCN and Cl heterobridges [Cu4(DNP)(SCN)Cl4]n ( 1 ) [DNP = 2,6‐bis(1,8‐naphthyridine‐2‐yl)pyridine] was solvothermally synthesized and employed as a dual‐functional co‐photocatalyst. Resulting from a narrowed band‐gap of 1.07 eV with suitable redox potential and unsaturated CuI/II sites, the complex together with H2O2 can effectively degrade Rhodamine B and methyl orange up to 87.4 and 88.2 %, respectively. Meanwhile, the complex mixed with H2PtCl6 can also accelerate the photocatalytic water splitting in the absence of a photosensitizer with the hydrogen production rate of 27.5 μmol · g–1 · h–1. These interesting findings may provide informative hints for the design of the multiple responsive photocatalysts.  相似文献   
10.
染料敏化光电化学电池(DSPECs)是构建人工光合作用体系的潜在方式,其优势在于可通过优化染料结构来拓展可见光吸收范围,从根本上提高太阳能利用效率.染料敏化光阳极在受激发产生电荷分离之后,激发电子注入TiO2半导体导带,由于其导带位置比传统的可见光半导体,如BiVO4和Fe3O4等相比较负,因此理论上可以在较小的偏压下取得较大的光电转换效率,也更有利于和光阴极相耦合实现无偏压分解水.电荷传输动力学研究表明,注入到TiO2导带的电子向氧化态光敏剂和催化剂的回传是造成体系能量损失的主要原因,集中体现在光电流密度和效率的降低.目前,已经报道了多种手段来减少DSPECs光阳极表面的电子回传,包括使用带有长烷基链的锚定基团对水氧化催化剂进行修饰,在半导体表面引入电子中介体以及使用核-壳结构的基底等.其中,SnO2/TiO2基底被广泛应用在染料敏化光阳极中,这种基底可以提高光生电子的注入效率,同时两种金属氧化物之间的异质结有效抑制了电子回传,从而提高了DSPECs的光电活性.然而,核-壳结构基底需要使用原子层沉积技术来制备,所以操作相对复杂.本文基于Ru-bda(bda=2,2'-联吡啶-6,6'-二羧酸)结构的分子水氧化催化剂和带有磷酸修饰基团的三联吡啶钌通过共吸附的方式制备染料敏化光阳极,在不使用核-壳结构基底的情况下,利用吡啶衍生物对TiO2电极表面的修饰来减少电子回传.本文利用一系列吡啶衍生物作修饰负载在TiO2光阳极上(TiO2|RuP,1;RuP=Ru(4,4'-(PO3H2)2-2,2'-联吡啶)(2,2'-联吡啶)2;1=Ru(bda)(L)2,bda=2,2'-联吡啶-6,6'-二羧酸,L=(10-吡啶-4-基氧基)癸基)膦酸.在100 mW/cm2的白光照射下(λ>400 nm),TiO2|RuP,1,P1(P1=4-羟基吡啶)光阳极在0.4 V(vs.NHE)的外加偏压下获得了1 mA/cm2的光电流密度,其光电流比未修饰吡啶的光阳极增加了42%.同时,其入射光子-电流转化效率在470 nm波长的单色光光照下达到最大,为13.6%.经过吡啶衍生物所修饰的光阳极光电性能和文献中利用核-壳结构基底所制备的类似光阳极性能相当,且光电流密度随吡啶对位取代基供电性能的增强而增大.瞬态吸收光谱和电化学阻抗谱测试表明,吡啶吸附在光阳极上能有效地抑制界面上的电子回传,延长电荷分离寿命,是光电流增加的根本原因,这也表明有机小分子修饰是提高染料敏化光阳极性能的简单、有效的策略.  相似文献   
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