Sharif Digital Repository

Leveraging subwavelength resonant nanostructures, plasmonic metasurfaces have recently attracted much attention as a breakthrough concept for engineering optical waves both spatially and spectrally. However, inherent ohmic losses concomitant with low coupling efficiencies pose fundamental impediments over their practical applications. Not only can all-dielectric metasurfaces tackle such substantial drawbacks, but also their CMOS-compatible configurations support both Mie resonances that are invariant to the incident angle. Here, we report on a transmittive metasurface comprising arrayed silicon nanodisks embedded in a homogeneous dielectric medium to manipulate phase and amplitude of... 

In this study a more precise formulation of electrical capacitance for a cylindrical capacitive sensor is reported. By using different theoretical models such as Coulomb law, Gauss law and Laplace equation the electrical capacitance is calculated. Based on the given models the relation between the capacitance and the geometrical parameters (e.g., cylindrical length) is formulated and by using suitable software capacitance variation is computed and compared for different methods. In Coulomb method, the electrical potential is first solved numerically by using Mathematica and then the electrical capacitance is computed. It is found that the active capacitor length is crucial parameter in the... 

In this paper, a mathematical modeling of a microcantilever gyroscope is presented considering the nonlinearities of the system due to electrostatic forces, fringing field, geometry and the inertial terms. The microgyroscope is actuated and detected by electrostatic methods and subjected to coupled bending oscillations. First a system of two nonlinear integro-differential equations is derived which describes flexural-flexural motion of electrostatically actuated and detected microbeam gyroscopes. Afterward, static deflection and pull-in instability of the microgyroscopes acted upon by DC voltages in both (driving and sensing) directions are studied for different parameters. The model's... 

Many of the physical macroscopic quantities could be explained as the result of a collection of microscopic particles which act independent of each-other, in a linear fashion. Since the physical laws of the interaction of these particles with their surrounding medium are non-deterministic, one could think of these particles as the generators of a linear stochastic field. In this paper, we have introduced a derivation which has yielded an equation for the spatiotemporal correlations in such a field. The derivation is simple and extendable to include the behavior of many physical particles. A simple numerical algorithm has been devised to solve the obtained initial value integrodifferential... 

In this study, the static deflection and pull-in instability of the doubly clamped microbeam with a mass attached to its midpoint are investigated. Nonlinear electrostatic forces, fringing fields, base rotation and mid-plane stretching of the beam in this model are considered. First, a system of two nonlinear integro-differential equations are expressed in partial derivatives which describe coupled flexural-flexural motion of electrostatically actuated microbeam gyroscopes under rotation. Then static deflection and pull-in instability of the microgyroscopes acted upon by DC voltages in both (direction and sensing) directions are studied. The equations of static motion are reduced by... 

The most suitable and widely used numerical integration method for boundary integrals in the BEM method is Gauss-Legendre integration. But, this integration method is not appropriate for singular and nearly singular integrations in BEM. In this study, some criteria are introduced for recognizing nearly singular integrals in the integral form of the Laplace equation. At the first stage, a criterion is obtained for the constant element and, at the later stages, higher order elements are investigated. In the present research, the Romberg integration method is used for nearly singular integrals. The results of this numerical method have good agreement with analytical integration. The singular... 

In this paper, we propose a new derivative-free preconditioned conjugate gradient method in order for solving large-scale square and under-determined nonlinear systems of equations. The proposed method is also equipped with a relaxed nonmonotone line search technique. Under some suitable assumptions, the global convergence property is established. Numerical results on some square and under-determined test systems show the efficiency and effectiveness of the new method in practice. An application of the new method for solving nonlinear integro-differential equations is also provided. © 2016 Elsevier Ltd  

Traditional analog computers that perform mathematical operations electronically or mechanically suffer from their relatively large size and slow response. Recently, the idea of spatial analog optical computing has overcome these restrictions. The different techniques to implement spatial analog optical computation can be categorized into two fundamental approaches: (I) metasurface (MS) approach and (II) Green's function (GF) approach. In the first approach, a metasurface is designed to implement the Green's function of the desired operator in the spatial domain. This means that this approach needs two sub-blocks to perform Fourier and inverse Fourier transform. On the other hand, in the... 

The present study examines the performance of three powerful methods including the original differential evolution (DE), the improved differential evolution (IDE), and the winner of the CEC-2014 competition, LSHADE, in addition to the covariance matrix adaptation evolution strategy (CMAES) for size optimization of truss structures under natural frequency constraints. Despite the abundant researches on novel meta-heuristic algorithms in the literature, the application of CMAES, one of the most powerful and reliable optimization algorithms, on the optimal solution of the truss structures has received scant attention. For consistent comparison between these algorithms, four stopping criteria... 

Profile analysis tensiometry (PAT) is presently the most frequently used technique for measuring surface tensions of liquids. The basis of this methodology is however an equilibrium force balance as given by the Gauss-Laplace equation. Therefore, its application under dynamic conditions, i.e. for growing drops or bubbles, is questionable. We discuss the limits of the applicability of PAT under dynamic conditions by using a growing drop configuration equipped with a high speed video camera. The systems studied are the water/air and water/hexane interface. The obtained "dynamic" drop profiles are analyzed by fitting the classical Gauss-Laplace equation. The results are additionally compared...