Birkhoff系统约化的Routh方法

研究Birkhoff系统的约化.首先,列出系统的运动微分方程及其循环积分;其次,构造Birkhoff系统的Routh函数组,利用循环积分约化Birkhoff系统的运动微分方程,并使约化后的动力学方程仍保持Birkhoff方程的形式;最后,举例说明结果的应用. 关键词： Birkhoff系统 约化 循环积分     

Ultrasound-assisted fabrication of metal nano-porous shells across polymer beads and their catalytic activity for reduction of 4-nitrophenol

Metal nano-porous architectures are a novel class of nanomaterials which has been applied in the fields of catalysis, sensing and gas storage because of their high surface-to-volume ratio, high mechanical strength and long-range ordered architectures. A commonly-used synthetic strategies to achieve architectures with high precision and diverse porosity design is the seed-and-growth method. In this work, using a dual-frequency sequential sonication approach, we have demonstrated a sonochemical-assisted one-pot seeding with a successive shell growth synthetic strategy for mesoporous metal deposition via a gold (Au) nanoparticle and poly(styrene) beads system. A uniform coating of gold nanoparticle seeds with dense surface coverage was formed by first employing 300 kHz ultrasound irradiation while the nano-porous shell growth was then performed under 1 MHz ultrasonic frequency. The precise control over the process conditions and parameters allowed for the design of well-defined shell thicknesses and surface roughness and area. The catalytic property of the MNMs was evaluated for the degradation of 4-nitrophenol and a high catalytic activity was achieved for the most porous gold structures, suggesting synergistic effects between the architecture of the nanomaterials and their surface reactivity.     

Are Two Metal Ions Better than One? Mono- and Binuclear α-Diimine-Re(CO)3 Complexes with Proton-Responsive Ligands in CO2 Reduction Catalysis

Here, the reduction chemistry of mono- and binuclear α-diimine-Re(CO)₃ complexes with proton responsive ligands and their application in the electrochemically-driven CO₂ reduction catalysis are presented. The work was aimed to investigate the impact of 1) two metal ions in close proximity and 2) an internal proton source on catalysis. Therefore, three different Re complexes, a binuclear one with a central phenol unit, 3 , and two mononuclear, one having a central phenol unit, 1 , and one with a methoxy unit, 2 , were utilised. All complexes are active in the CO₂-to-CO conversion and CO is always the major product. The catalytic rate constant k_cat for all three complexes is much higher and the overpotential is lower in DMF/water mixtures than in pure DMF (DMF=N,N-dimethylformamide). Cyclic voltammetry (CV) studies in the absence of substrate revealed that this is due to an accelerated chloride ion loss after initial reduction in DMF/water mixtures in comparison to pure DMF. Chloride ion loss is necessary for subsequent CO₂ binding and this step is around ten times faster in the presence of water [ 2 : k^Cl(DMF)≈1.7 s⁻¹; k^Cl(DMF/H₂O)≈20 s⁻¹]. The binuclear complex 3 with a proton responsive phenol unit is more active than the mononuclear complexes. In the presence of water, the observed rate constant k_obs for 3 is four times higher than of 2 , in the absence of water even ten times. Thus, the two metal centres are beneficial for catalysis. Lastly, the investigation showed that the phenol unit has no impact on the rate of the catalysis, it even slows down the CO₂-to-CO conversion. This is due to an unproductive, competitive side reaction: After initial reduction, 1 and 3 loose either Cl⁻ or undergo a reductive OH deprotonation forming a phenolate unit. The phenolate could bind to the metal centre blocking the sixth coordination site for CO₂ activation. In DMF, O−H bond breaking and Cl⁻ ion loss have similar rate constants [ 1 : k^Cl(DMF)≈2 s⁻¹, k^OH≈1.5 s⁻¹], in water/DMF Cl⁻ loss is much faster. Thus, the effect on the catalytic rate is more pronounced in DMF. However, the acidic protons lower the overpotential of the catalysis by about 150 mV.     

Bioinspired Transition-Metal Complexes as Electrocatalysts for the Oxygen Reduction Reaction

The oxygen reduction reaction (ORR) is one of the most important reactions in life processes and energy conversion systems. To alleviate global warming and the energy crisis, the development of high-performance electrocatalysts for the ORR for application in energy conversion and storage devices such as metal–air batteries and fuel cells is highly desirable. Inspired by the biological oxygen activation/reduction process associated with heme- and multicopper-containing metalloenzymes, iron and copper-based transition-metal complexes have been extensively explored as ORR electrocatalysts. Herein, an outline into recent progress on non-precious-metal electrocatalysts for the ORR is provided; these electrocatalysts do not require pyrolysis treatment, which is regarded as desirable from the viewpoint of bioinspired molecular catalyst design, focusing on iron/cobalt macrocycles (porphyrins, phthalocyanines, and corroles) and copper complexes in which the ORR activity is tuned by ligand variation/substitution, the method of catalyst immobilization, and the underlying supporting materials. Current challenges and exciting imminent developments in bioinspired ORR electrocatalysts are summarized and proposed.     

Nonintrusive data-based learning of a switched control heating system using POD,DMD and ANN

The aim of this work is to derive an accurate model of two-dimensional switched control heating system from data generated by a Finite Element solver. The nonintrusive approach should be able to capture both temperature fields, dynamics and the underlying switching control rule. To achieve this goal, the algorithm proposed in this paper will make use of three main ingredients: proper orthogonal decomposition (POD), dynamic mode decomposition (DMD) and artificial neural networks (ANN). Some numerical results will be presented and compared to the high-fidelity numerical solutions to demonstrate the capability of the method to reproduce the dynamics.     

Global Pathway Analysis: a hierarchical framework to understand complex chemical kinetics

An automated hierarchical framework, Global Pathway Analysis (GPA), is presented to understand complex chemical kinetics. The behaviour of the reacting system at macro level is bridged to the elementary reaction level by Global Pathways, which are the chemical pathways from an initial reactant species to a final product species. For each Global Pathway, its dominancy and effect on the system, such as those on the production or consumption of radicals, are quantified to understand its contribution to the system. Four examples are presented as demonstration: First, the classical second explosion limit of hydrogen is found to be resulted from the change of dominancy of a pressure-dependent Global Pathway, which consumes radical via H?+?O₂?+?M?=?HO₂?+?M reaction. Next, it is found that the negative temperature coefficient (NTC) regime of n-heptane is resulted from the competition between a low-temperature Global Pathway and a high-temperature Global Pathway. Third, a non-monotonic relation between autoignition delays and toluene ratio in toluene/n-decane mixture is analysed. This automated framework has been placed in public domain. Reduced kinetic models can be generated based on Global Pathways too. Finally, this methodology is demonstrated using DNS simulation results of the extinction and re-ignition of a turbulent non-premixed flame. The differences between simulation results are investigated using two different kinetics models via the analysis of global pathways.     

Core-shell microgel stabilized silver nanoparticles for catalytic reduction of aryl nitro compounds

Silver nanoparticles loaded into shell of poly (styrene-N-isopropylmethacrylamide-co-acrylic acid) core shell [P (SNA-CS)] gel particles were synthesized and analyzed by Fourier transform infrared spectroscopy (FTIR), transmission electron microscopy (TEM), ultraviolet–visible spectroscopy (UV–vis) and dynamic light scattering (DLS). Catalytic activity of Ag@P (SNA-CS) particles was investigated by reducing p-nitroaniline (p-NA) into p-aminoaniline (p-AA) in the presence of sodium borohydride (NaBH₄) reductant. Molecules of the substrate adsorbed on the surface of silver nanoparticles interact with borohydride ions (BH₄⁻) to form p-AA. Other nitroarenes like o-nitroaniline (o-NA), p-nitrophenol (p-NP) o-nitrophenol (o-NP), 2,4-dinitrophenol(2,4-DNP) were also reduced into their corresponding aryl amines using Ag@P (SNA-CS) composite microgels as catalyst. Reported catalyst efficiently reduced the nitro aromatic compounds individually as well as simultaneously at ambient temperature. Effect of different reaction conditions (catalyst dose, concentration of NaBH₄ and concentration of p-NA) on reaction completion time, value of apparent rate constant (k_app) and reduction efficiency of the catalyst for reduction of p-NA was also demonstrated. Ag@P (SNA-CS) catalyst was found to be able to retain activity up to four cycles.     

Hexagonal La2O3 Nanocrystals Chemically Coupled with Nitrogen-Doped Porous Carbon as Efficient Catalysts for the Oxygen Reduction Reaction

The construction of nano-scale hybrid materials with a smart interfacial structure, established by using rare earth oxides and carbon as building blocks, is essential for the development of economical and efficient catalysts for oxygen reduction reactions (ORRs). In this work, hexagonal La₂O₃ nanocrystals on a nitrogen-doped porous carbon (NPC) derived from crop radish, served as building bricks, are prepared by chemical precipitation and then calcination at elevated temperatures. The obtained La₂O₃/NPC hybrid exhibits a very high ORR activity with a half-wave potential of 0.90 V, exceeding that of commercial Pt/C (0.83 V). Both DFT theoretical and experimental results have verified that the significantly enhanced catalytic performance is ascribed to the formation of the C−O−La covalent bonds between carbon and La₂O₃. Through the covalent bonds, electrons can transfer from the carbon to La₂O₃ and occupy the unfilled e_g orbital of the La₂O₃ phase. This results in the accelerated adsorption of active oxygen and the facilitated desorption of the surface hydroxides (OH_ad⁻), thereby promoting the ORR over the catalyst.