Analytical modeling of static behavior of electrostatically actuatednano/micromirrors considering van der Waals forces

In this paper, the effect of van der Waals （vdW） force on the pull-in behavior of electrostatically actuated nano/micromirrors is investigated. First, the minimum po- tential energy principle is utilized to find the equation gov- erning the static behavior of nano/micromirror under electro- static and vdW forces. Then, the stability of static equilib- rium points is analyzed using the energy method. It is found that when there exist two equilibrium points, the smaller one is stable and the larger one is unstable. The effects of dif- ferent design parameters on the mirror＇s pull-in angle and pull-in voltage are studied and it is found that vdW force can considerably reduce the stability limit of the mirror. At the end, the nonlinear equilibrium equation is solved numer- ically and analytically using homotopy perturbation method （HPM）. It is observed that a sixth order perturbation approx- imation can precisely model the mirror＇s behavior. The re- suits of this paper can be used for stable operation design and safe fabrication of torsional nano/micro actuators.

EXPECTED DISCOUNTED PENALTY FUNCTION AT RUIN FOR RISK PROCESS PERTURBED BY DIFFUSION UNDER INTEREST FORCE

In this article, the risk process perturbed by diffusion under interest force is considered, the continuity and twice continuous differentiability for Фδ（u,w） are discussed,the Feller expression and the integro-differential equation satisfied by Фδ （u ,w） are derived. Finally, the decomposition of Фδ（u,w） is discussed, and some properties of each decomposed part of Фδ（u,w） are obtained. The results can be reduced to some ones in Gerber and Landry＇s,Tsai and Willmot＇s, and Wang＇s works by letting parameter δ and （or） a be zero.

IMPROVEMENTS ON THE ARC-LENGTH-TYPE METHOD

Arc-length-type and energy-type methods are two main strategies used in structural nonlinear tracing analysis, but the former is widely used due to the explicitness and clarity in conception, as well as the convenience and reliability in calculation. It is very important to trace the complete load-deflection path in order to know comprehensively the characteristics of structures subjected to loads. Unfortunately, the nonlinear analysis techniques are only workable for tracing the limit-point-type equilibrium path. For the bifurcation-point-type path, most of them cannot secure a satisfactory result. In this paper, main arc-length-type methods are reviewed and compared, and the possible reasons of failures in tracing analysis are briefly discussed. Some improvements are proposed, a displacement perturbation method and a force perturbation method are presented for tracing the bifurcation-point-type paths. Finally, two examples are analyzed to verify the ideas, and some conclusions are drawn with respect to the arc-length-type methods.

Diagnosis of the Forcing of Inertial-gravity Waves in a Severe Convection System

The non-hydrostatic wave equation set in Cartesian coordinates is rearranged to gain insight into wave generation in a mesoscale severe convection system. The wave equation is characterized by a wave operator on the lhs, and forcing involving three terms—linear and nonlinear terms, and diabatic heating—on the rhs. The equation was applied to a case of severe convection that occurred in East China. The calculation with simulation data showed that the diabatic forcing and linear and nonlinear forcing presented large magnitude at different altitudes in the severe convection region. Further analysis revealed the diabatic forcing due to condensational latent heating had an important influence on the generation of gravity waves in the middle and lower levels. The linear forcing resulting from the Laplacian of potential-temperature linear forcing was dominant in the middle and upper levels. The nonlinear forcing was determined by the Laplacian of potential-temperature nonlinear forcing. Therefore, the forcing of gravity waves was closely associated with the thermodynamic processes in the severe convection case. The reason may be that, besides the vertical component of pressure gradient force, the vertical oscillation of atmospheric particles was dominated by the buoyancy for inertial gravity waves. The latent heating and potential-temperature linear and nonlinear forcing played an important role in the buoyancy tendency. Consequently, these thermodynamic elements influenced the evolution of inertial-gravity waves.