The parameter diversity effect in coupled nonidentical elements has attracted persistent interest in nonlinear dynamics. Of fundamental importance is the so-called optimal configuration problem for how the spatial pos...The parameter diversity effect in coupled nonidentical elements has attracted persistent interest in nonlinear dynamics. Of fundamental importance is the so-called optimal configuration problem for how the spatial position of elements with different parameters precisely determines the dynamics of the whole system. In this work, we study the optimal configuration problem for the vibration spectra in the classical mass-spring model with a ring configuration, paying particular attention to how the configuration of different masses affects the second smallest vibration frequency （ω2） and the largest one （ωN）. For the extreme values of ω2 and ωN, namely, （ω2）min, （ω2）max, （ωN）min, and （ωN）max, we find some explicit organization rules for the optimal configurations and some approximation rules when the explicit organization rules are not available. The different distributions of ω2 and ωN are compared. These findings are interesting and valuable for uncovering the underlying mechanism of the parameter diversity effect in more general cases.展开更多
The optimized geometries at the RHF/6-311++G** level, the relatively stable energy at the MPW1PW91/6-311++G** level and the structural characters of anions have been acquired, indicating the stability is related to ...The optimized geometries at the RHF/6-311++G** level, the relatively stable energy at the MPW1PW91/6-311++G** level and the structural characters of anions have been acquired, indicating the stability is related to the chemical bonding of μ2?P atoms and the distri- bution of negative charges. The configurations of cage units P8 4- and P9 5- are stable due to the less torsion, but their ES values are relatively higher than that of P7 3- with more μ2?P atoms and the isolated stability is lower than that of P7 . They potentially play an important role as intermediate 3- in chemical reaction of producing complicated polyphosphides. Based on the related electronic properties, a stable polyanion must have low valence electron concentration, no (μ2?P)?(μ2?P) bond and a little dispersive charge. The earmark IR frequencies of cage units have been assigned to the vibration models in the end.展开更多
The paper discusses geometrical characteristics and strength parameters of fan blades equipped with replaceable active part it end ended to improve the fan adjustability owing to replacement or removal of the active p...The paper discusses geometrical characteristics and strength parameters of fan blades equipped with replaceable active part it end ended to improve the fan adjustability owing to replacement or removal of the active part, which allows the fan to maintain a wide range of ventilation modes.展开更多
基金Acknowledgements This work was supported by the National Natural Science Foundation of China under Grant Nos. 11075202 and 11475253.
文摘The parameter diversity effect in coupled nonidentical elements has attracted persistent interest in nonlinear dynamics. Of fundamental importance is the so-called optimal configuration problem for how the spatial position of elements with different parameters precisely determines the dynamics of the whole system. In this work, we study the optimal configuration problem for the vibration spectra in the classical mass-spring model with a ring configuration, paying particular attention to how the configuration of different masses affects the second smallest vibration frequency （ω2） and the largest one （ωN）. For the extreme values of ω2 and ωN, namely, （ω2）min, （ω2）max, （ωN）min, and （ωN）max, we find some explicit organization rules for the optimal configurations and some approximation rules when the explicit organization rules are not available. The different distributions of ω2 and ωN are compared. These findings are interesting and valuable for uncovering the underlying mechanism of the parameter diversity effect in more general cases.
文摘The optimized geometries at the RHF/6-311++G** level, the relatively stable energy at the MPW1PW91/6-311++G** level and the structural characters of anions have been acquired, indicating the stability is related to the chemical bonding of μ2?P atoms and the distri- bution of negative charges. The configurations of cage units P8 4- and P9 5- are stable due to the less torsion, but their ES values are relatively higher than that of P7 3- with more μ2?P atoms and the isolated stability is lower than that of P7 . They potentially play an important role as intermediate 3- in chemical reaction of producing complicated polyphosphides. Based on the related electronic properties, a stable polyanion must have low valence electron concentration, no (μ2?P)?(μ2?P) bond and a little dispersive charge. The earmark IR frequencies of cage units have been assigned to the vibration models in the end.
文摘The paper discusses geometrical characteristics and strength parameters of fan blades equipped with replaceable active part it end ended to improve the fan adjustability owing to replacement or removal of the active part, which allows the fan to maintain a wide range of ventilation modes.
