Fluctuating paths of least time, Schrödinger equation, van der Waals torque and Casimir effect mechanism

The use of an infinity of fluctuating paths of least time that are compatible with the quantum mechanics indeterminacy provides a new interpretation in geometrical optic of the interference pattern of Young’s double slit experiment, which suggests that the wave behavior of matter and radiation is dictated by the space-time geodesics. Moreover, the association of a wave function to each path of least time as a probability amplitude together with an uncertainty for momentum and position allows to derive the Schrödinger’s equation starting from the geodesic’s characteristics. A new insight is obtained regarding the van der Waals torque as well as Casimir attraction/repulsion mechanism.

Debye vs. Casimir: controlling the structure of charged nanoparticles deposited on a substrate

Multiscale simulations and experiments show how to control the structure of deposited nanoparticles by combining the Debye-screened electrostatic repulsion and critical Casimir attraction.

A corrected model for static and dynamic electromechanical instability of narrow nanotweezers: Incorporation of size effect, surface layer and finite dimensions

Herein, a corrected theoretical model is proposed for modeling the static and dynamic behavior of electrostatically actuated narrow-width nanotweezers considering the correction due to finite dimensions, size dependency and surface energy. The Gurtin–Murdoch surface elasticity in conjunction with the modified couple stress theory is employed to consider the coupling effect of surface stresses and size phenomenon. In addition, the model accounts for the external force corrections by incorporating the impact of narrow width on the distribution of Casimir attraction, van der Waals (vdW) force and the fringing field effect. The proposed model is beneficial for the precise modeling of the narrow nanotweezers in nano-scale.

Instability Characteristics of Free-Standing Nanowires Based on the Strain Gradient Theory with the Consideration of Casimir Attraction and Surface Effects

Size-dependent dynamic instability of cylindrical nanowires incorporating the effects of Casimir attraction and surface energy is presented in this research work. To develop the attractive intermolecular force between the nanowire and its substrate, theproximity force approximation(PFA) for small separations, and the Dirichlet asymptotic approximation for large separations with a cylinder-plate geometry are employed. A nonlinear governing equation of motion for free-standing nanowires – based on the Gurtin-Murdoch model – and a strain gradient elasticity theory are derived. To overcome the complexity of the nonlinear problem in hand, a Garlerkin-based projection procedure for construction of a reduced-order model is implemented as a way of discretization of the governing differential equation. The effects of length-scale parameter, surface energy and vacuum fluctuations on the dynamic instability threshold and adhesion of nanowires are examined. It is demonstrated that in the absence of any actuation, a nanowire might behave unstably, due to the Casimir induction force.

Using strain gradient elasticity in conjunction with Gurtin–Murdoch theory for modeling the coupled effects of surface and size phenomena on the instability of narrow nano-switch

While comprehensive researches have been conducted on modeling the electromechanical stability of wide-enough beam-plate nano-switches, few researchers have focused on modeling the electromechanical instability of narrow-width nano-switches. For such systems, considering the coupled effects of surface stresses and size dependency of material characteristics is crucial as well as applying appropriate force models. In this paper, Gurtin–Murdoch surface theory incorporating with strain gradient elasticity is employed to study the pull-in instability of narrow-width beam-type nano-switch with small width to height ratio. The model accounts for the force corrections, i.e. the impact of finite dimensions on the fringing field, Casimir attraction and van der Waals force. Furthermore, a modified gas damping model has been incorporated in the governing equation. The nonlinear governing equation was solved using analytical Rayleigh–Ritz method. The influences of the above-mentioned corrections on the static and dynamic pull-in parameters, phase planes and stability threshold of the switch are demonstrated. The modified model is compared with conventional parallel beam-plate models in the literature.

Size-Dependent Dynamic Behavior and Instability Analysis of Nano-Scale Rotational Varactor in the Presence of Casimir Attraction

When the size of structures approaches to the sub-micron scale, physical responses of such systems become size-dependent, hence, classic theories may not be able to predict the behavior of the miniature structures. In the present article, the modified couple stress theory (MCST) is employed to account for the effect of the size-dependency on the dynamic instability of torsional nano-electromechanical systems (NEMS) varactor. By incorporating the Coulomb, Casimir and damping forces, the dimensionless governing equations are derived. The influences of Casimir force, applied voltage and length scale parameter on the dynamic behavior and stability of fixed points are investigated by plotting the phase portrait and bifurcation diagrams. It is found that the Casimir force reduces the instability threshold of the systems and the small-scale parameter enhances the torsional stability. The pull-in instability phenomenon shows the saddle-node bifurcation for torsional nano-varactor.

Influence of Accelerating Force on the Electromechanical Instability of Paddle-Type and Double-Sided Sensors Made of Nanowires

The double-sided and paddle-type nanostructures are promising for developing miniature accelerometers. In the present work, the impact of the accelerating force on the pull-in performance of the double-sided and paddle-type sensors fabricated from nanowire are investigated. The proximity force approximation (PFA) is employed to consider the effect of Casimir attraction in the theoretical model. Using the modified couple stress theory, the constitutive equations of the sensors are derived. The governing equations are solved by two different approaches, i.e. modified variational iteration method (MVIM), and finite difference method (FDM). The influences of the Casimir and accelerating forces, geometrical parameters and the size phenomenon on the pull-in parameters are demonstrated.