Graphene-based mass sensors: Chaotic dynamics analysis using the nonlocal strain gradient model

Nonlinear oscillations of graphene resonators are unavoidable due to enhancing the mass sensitivity of graphene-based mass sensors and the nonlinear behavior of the systems provides the route to chaos. In this paper, the nonlinear and chaotic behavior of the graphene-based mass sensor is investigated. The nano-mechanical sensor includes an electrostatically actuated fully clamped single-graphene sheet as a nano-resonator with an attached concentrated mass. By neglecting the rotary inertia, the equation of motion of the nano- resonator and the attached mass is derived using the nonlocal strain gradient theory of elasticity. The nano-resonator is modeled as a Kirchhoff nano-plate with the von Kármán-type geometric nonlinearity. Applying the Galerkin decomposition method to the partial differential equation of motion leads to the ordinary differential equation. Based on the Melnikov's integral method two analytical criteria are derived which provide necessary conditions that determine the chaotic region of the system. The chaotic dynamics of the system are also scrutinized and verified through plotting the Lyapunov exponent diagram, phase plane trajectories and Poincaré maps.     

Noise-induced bistable switching dynamics through a potential energy landscape

Interlinked positive feedback loops,an important building block of biochemical systems,can induce bistable switching,leading to long-lasting state changes by brief stimuli.In this work,prevalent mutual activation between two species as another positive feedback is added to a generic interlinked positive-feedback-loop model originating from many realistic biological circuits.A stochastic fluctuation of the positive feedback strength is introduced in a bistable interval of the feedback strength,and bistability appears for the moderate feedback strength at a certain noise level.Stability analysis based on the potential energy landscape is further utilized to explore the noise-induced switching behavior of two stable steady states.     

Asymptotic Formulas and Inequalities for the Gamma Function in Terms of the Tri-Gamma Function

Results in Mathematics - In the paper, the authors establish some asymptotic formulas and double inequalities for the factorial n! and the gamma function Γ in terms of the tri-gamma function...     

含镨稀土抛光粉的制备及其抛光性能研究

通过采用碳酸镧(铈、镨)为前驱体,经氟化、高温焙烧、机械湿磨的方法得到稀土抛光粉,研究了不同掺镨量对稀土抛光粉的物相结构、表面形貌、粒度、密度、抛蚀量的影响。通过XRD分析得出结论:La2O3,Pr6O11固溶于CeO2的晶格结构中,并且出现了新的物相LaOF;随镨掺量的增大,LaOF的衍射峰强度不断增加,晶化程度不断增加;CeO2的XRD特征峰向左偏移,晶胞参数变大,晶面间距变大。通过粒度分析得出结论:随镨掺量的增加,抛光粉的中位粒径出现了先减小后增大的规律性变化。通过抛蚀量测试得出结论:随镨掺量的增加,抛光粉的抛蚀量出现了先增大后减小的变化。掺镨稀土抛光在镨含量为4.8%时,具有最小的中位粒径、较好的表面形貌和最大的抛蚀量。     

Nondimensional frequency scaling of aerodynamically-tensioned membranes

Membrane wings have applications that involve low Reynolds number flyers such as micro air vehicles. The time-averaged and time-dependent deformations of the membrane affect the aerodynamic characteristics of the wing, primarily in the region beyond the maximum aerodynamic efficiency of the wing. This paper investigates an appropriate nondimensional vibration frequency scaling of a spanwise tensioned membrane with free (unattached) leading and trailing edges at low Reynolds numbers relative to nondimensional aeroelastic parameters. Silicone rubber membranes with varying spanwise pre-tension, aerodynamic tension (due to wing angle-of-attack and flow dynamic pressure), modulus of elasticity, span, and thickness are studied. Experimental results are compared to a proposed scaling that simplifies the aerodynamic loading as a uniform pressure distribution acting on the membrane. Data is further compared and discussed relative to previous published results of membrane wings with finite wing spans (three-dimensional flow) and fixed (rigid) leading edges.     

Bilinear neural network method to obtain the exact analytical solutions of nonlinear partial differential equations and its application to p-gBKP equation

Nonlinear Dynamics - A new method named bilinear neural network is introduced in this paper, and the corresponding tensor formula is proposed to obtain the exact analytical solutions of nonlinear...     

REVIEW ON OPTIMIZATION OF ASTEROID CAPTURE ORBITS

小行星捕获对研究行星起源、地球生命来源、防御小行星撞击地球和开采行星矿产资源具有重要的意义。由于现有的推进器能力不足,小行星捕获任务中优化小行星捕获所需要的速度增量是任务成败的关键。本文分别从利用引力辅助轨道优化、连续小推力轨迹优化、小行星捕获任务轨道优化设计及小行星临时捕获等4 个方向介绍小行星捕获轨道优化方面国内外研究进展及现状。基于对上述研究现状的分析,尝试展望小行星捕获轨道优化研究的未来发展趋势。