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In this study, the surface discharge current pulses of polyetheretherketone (PEEK) material under positive repetitive square voltage in a nitrogen atmosphere are measured. The influences of different voltage amplitudes and frequencies on the detail parameters of forward discharge and backward discharge current pulses are statistically analysed. The results show that as the square voltage amplitude increases, the current pulse amplitude, fall time and pulse width of both forward and backward discharge current increase, and the rise time does not change significantly. As the voltage frequency increases, current pulse amplitude, fall time and pulse width of both forward and backward discharge current decrease, and the rise time does not change significantly. Due to the independence of the discharge at different repetitive cycles, the specific discharge process in one cycle is analysed in detail to explain the influence mechanism of the voltage amplitude and frequency on the discharge current. By mean of the Richardson–Schottky and the Cavallini relaxation model, the relationship between discharge voltage ratio and surface charge, and the decay process of surface discharge are analysed. Furthermore, the influences of amplitude and frequency of the positive repetitive square voltage on the PEEK surface current pulses are explained qualitatively.

Critical dynamic stress (σcri) and accumulative plastic strain (εp) are primary indicators regarding the dynamic stability of unbound granular materials (UGMs). This study aims to seek an effective method to evaluate the dynamic stability of UGMs used in railway subgrades. First, the dynamic characteristics of an UGM used in railway subgrade bed construction were investigated by performing a series of large-scale cyclic triaxial tests, with the results showing that εp versus cycle number (N) curves can be categorized into stable, failure, and critical patterns. Grey relational analyses were then established, where the analyzed results demonstrated that the εp–N curve pattern and final accumulative plastic strain (εs) of the stable curves are strongly correlated with the moisture content (w), confining pressure (σ3), and dynamic deviator stress (σd). The analyzed grey relational grades distributed in a narrow range of 0.72 to 0.81, indicating that w, σ3, and σd have similar degrees of importance on determining the εp–N curve patterns and the values of εs of the UGM. Finally, a data processing method using a back-propagation (BP) neural network is introduced to analyze the test data, and an empirical approach is developed to evaluate the σcri (considering the effects of σ3 and w) and εs (considering the effects of σ3, w, and σd) of the UGM. The analyzed results illustrated that the developed method can effectively reflect the linear/non-linear relationships of σcri and εs with respect to σ3 and/or σd. The σcri approximately increases linearly with increasing σ3, and a simple empirical formula is proposed for the σcri. In addition, εs and its variation rate increase non-linearly with increasing σd but decrease non-linearly as σ3 increases.

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Here we employ density functional theory calculations to systematically investigate the underlying mechanism of Cu(OTf) 2 -catalyzed [3+2] cycloaddition reactions in the synthesis of CF 3 -substituted pyrazolidines. About eight possible initial configurations of the [3+2] reaction is considered, and all relevant reactants, transition states, and products are optimized. Based on these structures, internal reaction coordinate paths, and wavefunction analysis results, we conclude that the Cu(OTf) 2 -catalyzed [3+2] cycloaddition follows a concerted asynchronous mechanism. The C N bond forms immediately after the formation of the C C bond. Among the eight reaction paths, the energy barrier for the [3+2] reaction that leads to the CF 3 -substituted synpyrazolidine is the lowest, $5.4 kcal/mol, which might result in the diastereoselectivity that is observed in the experiment. This work not only gives the detailed mechanism of the Cu(OTf) 2 -catalyzed [3+2] cycloaddition but can also be helpful for the future designation of Cu(OTf) 2 -based cycloaddition processes.

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