Stability analysis of electrostatic nanotweezers

In this paper, the pull-in instability of electrostatically actuated nanotweezers considering the dispersion forces is studied using distributed and lumped parameter models. By analogy to nanoswitches, closed-form solutions are obtained for electrostatic nanotweezers. The distributed and lumped parameter modeling of the tweezer result, respectively, in two coupled nonlinear boundary value problems and two coupled nonlinear equations, which are solved numerically in the cases of electrostatic microtweezers, freestanding nanotweezers, and electrostatic nanotweezers. In each case, analytical and numerical solutions are obtained and compared with those of the corresponding switch. In addition, the results of the distributed and lumped parameter models are compared. The detachment length and minimum initial gap of nanotweezers are determined.     

A new approach to the evaluation of Casimir and van der Waals forces in the transition region

This paper studies the incorporation of Casimir and van der Waals forces applied to a nanostructure with parallel configuration. The focus of this study is in a transition region in which Casimir force gradually transforms into van der Waals force. It is proposed that in the transition region, a proportion of both Casimir and van der Waals forces, as the interacting nanoscale forces, can be considered based on the separation distance between upper structure and substrate during deflection. Moreover, as the separation distance descends during deflection, the nanoscale forces could transform from Casimir to a proportion of both Casimir and van der Waals forces and so as to van der Waals. This is also extended to the entire surface of the nanostructure in such a way that any point of the structure may be subjected to Casimir, van der Waals or a proportion of both of them about its separation distance from the substrate. Therefore, a mathematical model is presented which calculate the incorporation of Casimir and van der Waals forces considering transition region and their own domination area. The mechanical behavior of a circular nano-plate has been investigated as a case study to illustrate how different approaches to nanoscale forces lead to different results. For this purpose, the pull-in phenomena and frequency response in terms of magnitude have been studied based on Eringen nonlocal elasticity theory. The results are presented using different values of the nonlocal parameter and indicated in comparison with those of the classical theory. These results also amplify the idea of studying the mechanical behavior of nanostructures using the nonlocal elasticity theory.     

On the dynamic instability of nanowire-fabricated electromechanical actuators in the Casimir regime: Coupled effects of surface energy and size dependency

Herein, the dynamic pull-in instability of cantilever nanoactuator fabricated from conductive cylindrical nanowire with circular cross-section is studied under the presence of Casimir force. The Gurtin–Murdoch surface elasticity in combination with the couple stress theory is employed to incorporate the coupled effects of surface energy and size phenomenon. Using Green–Lagrange strain, the higher order surface stress components are incorporated in the governing equation. The Dirichlet mode is considered and an asymptotic solution, based on the path integral approach, is applied to consider the effect of the Casimir attraction. Furthermore, the influence of structural damping is considered in the model. The nonlinear governing equation is solved using analytical reduced order method (ROM). The effects of various parameters on the dynamic pull-in parameters, phase planes and stability threshold of the actuator are demonstrated.     

Surface roughness influence on the pull-in voltage of microswitches in presence of thermal and quantum vacuum fluctuations

In this work we investigate the influence of the combined effect from random self-affine roughness, finite conductivity, and finite temperature on the pull-in voltage in microswitches influenced by thermal and quantum vacuum fluctuations through the Casimir force and electrostatic forces. It is shown that for separations within the micron or sub-micron range the roughness influence plays a dominant role, while temperature starts to show its influence well above micron separations. Indeed, increasing the temperature leads to higher pull-in voltages since it leads to an increased Casimir force. The temperature influence is more significant for relatively large roughness exponent H ∼ 1, while its influence is significantly lower with increasing lateral roughness correlation length ξ or due to long wavelength surface smoothness.     

Theoretical modeling of the Casimir force-induced instability in freestanding nanowires with circular cross-section

The Casimir force can induce instability and adhesion in freestanding nanostructures. Previous research efforts in this area have exclusively focused on modeling the instability in structures with planar or rectangular cross-section, while, to the best knowledge of the authors, no attention has been paid to investigate this phenomenon for nanowires with circular cross-section. In this study, effects of the Casimir force on the instability and adhesion of freestanding Cylinder–Plate and Cylinder–Cylinder geometries are investigated, which are commonly encountered in real nanodevices. To compute the Casimir force, two approaches, i.e. the proximity force approximation (PFA) for small separations and Dirichlet asymptotic approximation (scattering theory) for large separations, are considered. A continuum mechanics theory is employed, in conjunction with the Euler-beam model, to obtain constitutive equations of the systems. The governing nonlinear constitutive equations of the nanostructures are solved using two different approaches, i.e. the analytical modified Adomian decomposition (MAD) and the numerical finite difference method (FDM). The detachment length and minimum gap, both of which prevent the Casimir force-induced adhesion, are computed for both configurations.     

Comparing mechanical analysis with generalized-competitive-mode analysis for the plasma chaotic system

The plasma chaotic system is a dissipative dynamical system modeled by a parametric plasma instability arising from the interaction of the whistler and ion acoustic waves with the plasma oscillation near the lower hybrid resonance. The amplitudes of these three oscillations obey a three-dimensional system of ordinary differential equations that exhibits chaos for certain parameter values. Besides the maximal Lyapunov exponent technique, a generalized-competitive-mode (GCM) technique has been proposed to evaluate parameter values associated with chaos. A mechanical analysis has also been proposed to reveal the mechanisms underlying the different dynamical modes including chaos. In a series of comparisons between the GCM analysis and mechanical analysis, chaos for the plasma chaotic system is determined. The mechanism and causes by which the plasma chaotic system produces different dynamical behaviors are interpreted. Furthermore, using the whistler-parameter variation of the Casimir function and Casimir power for the plasma system, the generating mechanisms of the different orbital modes and the different levels of chaos are uncovered.     

Geometry and charge carrier induced stability in Casimir actuated nanodevices

In this work we demonstrate, that in Casimir actuated nanodevices, geometry and charge carriers concentration change the stability and the pull-in conditions that cause stiction. The stability is analyzed by calculating the bifurcation diagram of the capacitive switch as a function of plate thickness for Au and Si showing that previous calculations based on Lifshitz formula for half-spaces underestimated the stability conditions. Taking into account the size effect, we recalculate the bifurcation diagram for different metals and for Si with different carrier concentrations showing the change in the stability conditions.     

Casimir effects: an optical approach I. Foundations and examples

We present the foundations of a new approach to the Casimir effect based on classical ray optics. We show that a very useful approximation to the Casimir force between arbitrarily shaped smooth conductors can be obtained from knowledge of the paths of light rays that originate at points between these bodies and close on themselves. Although an approximation, the optical method is exact for flat bodies, and is surprisingly accurate and versatile. In this paper we present a self-contained derivation of our approximation, discuss its range of validity and possible improvements, and work out three examples in detail. The results are in excellent agreement with recent precise numerical analysis for the experimentally interesting configuration of a sphere opposite an infinite plane.     

The Shape of the Edge of a Leaf

Leaves and flowers frequently have a characteristic rippling pattern at their edges. Recent experiments found similar patterns in torn plastic. These patterns can be reproduced by imposing metrics upon thin sheets. The goal of this paper is to discuss a collection of analytical and numerical results for the shape of a sheet with a non-flat metric. First, a simple condition is found to determine when a stretched sheet folded into a cylinder loses axial symmetry, and buckles like a flower. General expressions are next found for the energy of stretched sheets, both in forms suitable for numerical investigation, and for analytical studies in the continuum. The bulk of the paper focuses upon long thin strips of material with a linear gradient in metric. In some special cases, the energy-minimizing shapes of such strips can be determined analytically. Euler–Lagrange equations are found which determine the shapes in general. The paper closes with numerical investigations of these equations.     

On the Possibility of the Implicit Renormalization of the Casimir Energy

We propose a procedure for renormalizing the Casimir energy that makes the steps that are used in the standard renormalization procedure, that is, regularization, subtraction, and deregularization, implicit. The proposed procedure is based on the calculation of a set of convergent sums, each of which is related to the initial divergent sum of the non-renormalized Casimir energy. Next, we construct a system of linear equations that relates this set of convergent sums to the renormalized Casimir energy. The unknown renormalized Casimir energy is obtained as a result of solving this system of equations. In this case, both the calculations of the convergent sums and the subsequent solution of the system of linear equations are performed with a certain (generally speaking, arbitrary) ordered accuracy; thus, the result is also approximate. The proposed procedure is, first, more computationally effective than the standard one, and, second, applicable not only to the problems where a transcendental equation for the spectrum can be written, but also to the problems where the spectrum is known only numerically.     

Extension of Operational Matrix Technique for the Solution of Nonlinear System of Caputo Fractional Differential Equations Subjected to Integral Type Boundary Constrains

We extend the operational matrices technique to design a spectral solution of nonlinear fractional differential equations (FDEs). The derivative is considered in the Caputo sense. The coupled system of two FDEs is considered, subjected to more generalized integral type conditions. The basis of our approach is the most simple orthogonal polynomials. Several new matrices are derived that have strong applications in the development of computational scheme. The scheme presented in this article is able to convert nonlinear coupled system of FDEs to an equivalent S-lvester type algebraic equation. The solution of the algebraic structure is constructed by converting the system into a complex Schur form. After conversion, the solution of the resultant triangular system is obtained and transformed back to construct the solution of algebraic structure. The solution of the matrix equation is used to construct the solution of the related nonlinear system of FDEs. The convergence of the proposed method is investigated analytically and verified experimentally through a wide variety of test problems.     

An improved model for the cantilever NEMS actuator including the surface energy,fringing field and Casimir effects

The influence of the surface energy on the instability of nano-structures under the electrostatic force has been investigated in recent years by different researchers. It appears that in all prior research, the response of all structures becomes softer due to the surface effects. In the present study, the pull-in instability of a NEMS device incorporating the electrostatic force and Casimir intermolecular attraction for different values of the surface parameter is investigated by the Duan–Rach method of determined coefficients (MDC) in order to identify the remarkable effect of the surface energy. Although the obtained results verify the behavior of such structures in presence of the fringing field and the Casimir attraction same as the previous investigations, however the incremental effects of the surface energy cause the aforementioned structures to behave more stiffly in contrast.     

斜直圆筒内基于Euler-Rodrigues参数的细长杆螺旋屈曲研究

基于Euler-Rodrigues参数描述受约束细杆的后屈曲变形状态,建立相应的能量泛函,导出非线性平衡微分方程及接触力表达式.采用有限元法对能量泛函进行分析计算,通过与现有文献中数值、理论结果比较,验证了公式和求解过程的正确性.结合算例,揭示了正弦屈曲模态与螺旋屈曲模态之间的转化过程,证实了在受约束细长杆的后屈曲响应中存在不同屈曲模态之间的互相转变.     

Focusing virtual photons: casimir energies for some pairs of conductors

We consider the Casimir energy E of a pair of conductors, E( parallel) for parallel plates, E(|o) for a plate and a sphere, E(oo) for two separated spheres, and E( middle dot in circle) for one sphere inside the other. We also obtain E((o) for an open shell and a sphere, a configuration which might be experimentally preferable. Semiclassically the Casimir energy is given by the optical properties of the system of coaxial mirrors, with focal lengths f(1) and f(2), a distance l相似文献   

Acoustic scattering by an elastic elliptic cylinder in water: numerical results and experiments

The acoustic scattering from an elastic elliptic cylinder immersed in water and excited by a normally incident plane wave is considered in this paper. The purpose is to determine, theoretically and experimentally, the pressure scattered by this cylinder. A model based on the theory of elasticity is described briefly. It consists in carrying out expansions in Fourier series of the expressions relating to the conditions of continuity (displacements and constraints) at the surface of cylinder. These expressions form a system of equations. The resolution of this system enables us to obtain the scattering coefficient, then the pressure scattered by the cylinder. The numerical results obtained from this model are compared with experimental results obtained by means of an experimental short-pulse method presented in the literature. An good agreement between the results is noted.     

Nonequilibrium electromagnetic fluctuations: heat transfer and interactions

The Casimir force between arbitrary objects in equilibrium is related to scattering from individual bodies. We extend this approach to heat transfer and Casimir forces in nonequilibrium cases where each body, and the environment, is at a different temperature. The formalism tracks the radiation from each body and its scatterings by the other objects. We discuss the radiation from a cylinder, emphasizing its polarized nature, and obtain the heat transfer between a sphere and a plate, demonstrating the validity of proximity transfer approximation at close separations and arbitrary temperatures.     

Models base study of inclined MHD of hybrid nanofluid flow over nonlinear stretching cylinder

Focus of the present analysis is on the stagnation point flow of hybrid nanofluid with inclined magnetic field over a moving cylinder. The extended version of two models (e.g. Xue model and Yamada-Ota model for hybrid nanofluids) are considered in this study). A mathematical model of hybrid nanofluid flow is developed under certain flow assumptions. Boundary layer approximations are also utilized to model a system of partial differential equations. The systems of partial differential equations are further converted to dimensionless systems of ordinary differential equations by means of suitable similarity transformations. A numerical solution is obtained by applying bv4c technique. Effects of variation in physical parameters involved are depicted through graphs. Skin friction coefficient and Nusselt number are highlighted through tables. Our main objective is to investigate the heat transfer rate on the surface of the nonlinear stretching cylinder. The results of Xue model and Yamada-Ota model for the hybrid nanofluid due to nonlinear stretching cylinder are computed for comparison. In both cases, velocity and temperature profiles are best compared to the decay results.     

场方法的改进及其在积分Riemann-Cartan空间运动方程中的应用

和Hamilton-Jacobi方法类似,Vujanovi?场方法把求解常微分方程组特解的问题转化为寻找一个一阶拟线性偏微分方程(基本偏微分方程)完全解的问题,但Vujanovi?场方法依赖于求出基本偏微分方程的完全解,而这通常是困难的,这就极大地限制了场方法的应用.本文将求解常微分方程组特解的Vujanovi?场方法改进为寻找动力学系统运动方程第一积分的场方法,并将这种方法应用于一阶线性非完整约束系统Riemann-Cartan位形空间运动方程的积分问题中.改进后的场方法指出,只要找到基本偏微分方程的包含m(m≤ n,n为基本偏微分方程中自变量的数目)个任意常数的解,就可以由此找到系统m个第一积分.特殊情况下,如果能够求出基本偏微分方程的完全解(完全解是m=n时的特例),那么就可以由此找到≤系统全部第一积分,从而完全确定系统的运动.Vujanovi?场方法等价于这种特殊情况.     

Free Vibration Analysis of Nanocomposite Plates Reinforced by Graded Carbon Nanotubes Based on First-Order Shear Deformation Plate Theory

Based on the Mindlin's first-order shear deformation plate theory this paper focuses on the free vibration behavior of functionally graded nanocomposite plates reinforced by aligned and straight single-walled carbon nanotubes (SWCNTs). The material properties of simply supported functionally graded carbon nanotube-reinforced (FGCNTR) plates are assumed to be graded in the thickness direction. The effective material properties at a point are estimated by either the Eshelby-Mori-Tanaka approach or the extended rule of mixture. Two types of symmetric carbon nanotubes (CNTs) volume fraction profiles are presented in this paper. The equations of motion and related boundary conditions are derived using the Hamilton's principle. A semi-analytical solution composed of generalized differential quadrature (GDQ) method, as an efficient and accurate numerical method, and series solution is adopted to solve the equations of motions. The primary contribution of the present work is to provide a comparative study of the natural frequencies obtained by extended rule of mixture and Eshelby-Mori-Tanaka method. The detailed parametric studies are carried out to study the influences various types of the CNTs volume fraction profiles, geometrical parameters and CNTs volume fraction on the free vibration characteristics of FGCNTR plates. The results reveal that the prediction methods of effective material properties have an insignificant influence of the variation of the frequency parameters with the plate aspect ratio and the CNTs volume fraction.     

The evolution of catalyst layer morphology and sub-surface growth of CNTs over the hot filament grown Fe-Cr thin films

In this study a hot filament chemical vapour deposition (HFCVD) technique was used to prepare Fe-Cr films on Si substrate as catalysts for thermal CVD (TCVD) growing of carbon nanotubes (CNTs) from liquid petroleum gas (LPG) at 800 °C. To characterize the catalysts or CNTs, X-ray photoelectron spectroscopy (XPS), scanning electron microscopy (SEM), transmission electron microscopy (TEM) and Raman spectroscopy were used. The XPS spectra obtained at different stages of Ar⁺ sputtering revealed that in the depth of catalyst layers, the relative Fe-Cr concentrations are higher than the top-surface. SEM images of samples after TCVD indicate a significant CNT growing at the backside of catalyst layer compared with its top which is accompanied with morphological changes on catalyst layer such as formation of cone-shape structures, rippling, cracking and rolling of the layer. These observations were attributed to the more catalytic activity of the sub-surface beside the poor activity of the top-surface as well as the presence of individual active islands over the surface of the catalyst thin film.