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Yongyong Cai & Yan Wang 《数学研究》2020,53(2):125-142
We consider the nonlinear Dirac equation (NLD) with time dependent external electro-magnetic potentials, involving a dimensionless parameter $εin(0,1]$ which is inversely proportional to the speed of light. In the nonrelativistic limit regime $εll1$ (speed of light tends to infinity), we decompose the solution into the eigenspaces associated with the 'free Dirac operator' and construct an approximation to the NLD with $O(ε^2)$ error. The NLD converges (with a phase factor) to a coupled nonlinear Schrödinger system (NLS) with external electric potential in the nonrelativistic limit as $εto0^+$, and the error of the NLS approximation is first order $O(ε)$. The constructed $O(ε^2)$ approximation is well-suited for numerical purposes. 相似文献
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Nanopore-based electrochemical technique is a promising tool for detecting single proteins. However, detecting single proteins using a nanopipette in their native state without labeling is challenging due to the rapid translocation, which results in an inefficient signal identification. In our study, we finely tuned the driving force equilibrium between electrophoretic force (EPF) and electroosmotic flow (EOF) inside the nanopipette for efficient sensing of single glucose oxidase (GOD) molecules. The duration time of GOD within the nanopipette is extended to about 4 ms. This strategy provided clear ionic current signals with a signal-to-noise ratio of 3.3. As EPF increased in the direction opposite to the motion of GOD, we observed a nonlinear growth in GOD’s duration time. This extended the duration to about 4.4 times longer at –1000 mV compared to at –800 mV. Hence, nanopore-based electrochemical sensing could be used for single GOD molecule analysis as an ultrasensitive method. 相似文献
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单原子催化体系的成功构建将催化领域研究深入到更小的尺度范围,不仅可以从原子层次认识复杂的多相催化反应,而且由于其优越的催化性能在工业催化中具有巨大的应用潜能。本文基于近年来国内外研究者在单原子催化领域的研究工作,总结归纳了单原子催化剂的性能特征,介绍了单原子催化剂的制备手段、表征技术、理论研究及其在CO氧化、选择性加氢和光电催化等反应中的应用研究进展,分析了单原子催化剂特殊的电子结构对催化性能和反应机理的影响及其作用机制,指出了单原子催化体系在研究领域取得的突破与不足,对于深刻认识单原子催化的概念与原理、完善实验与理论研究方法、拓展应用范围和尽早实现工业应用提出了建议与展望。 相似文献
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建立了非稳态油膜力、碰摩力作用下,偏角不对中轴系的横向振动模型,将Jeffcott转子模型推广至约束条件下的轴系振动模型,通过引入转子间的位移约束,由Lagrange方程导出了不对中轴系系统的振动方程.仿真研究表明:由于不对中的存在,轴系横向振动是强非线性、非定常、同时含有自激励、参数激励和外激励的三自由度振动系统;由于从动轴与主动轴的不对中,导致了转轴间的运动约束,使轴系横向振动系统比Jeffcott转子动力学模型所描述的振动系统少了一个自由度.随着偏角不对中量、转轴质量比的变化,系统出现周期、概周期、混沌运动特征.不对中轴系处于概周期运动时,呈现出自激振动特征.其结果可为旋转机械故障诊断、轴系对中及设备的安全运行提供更为准确的理论参考. 相似文献
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We are delighted to present this special issue in honor of Professor Jie Shen on the occasion of his sixtieth birthday in Journal of Mathematical Study (JMS) of... 相似文献