Sharif Digital Repository

In General, there are two methods to analyse the inverse kinematic of manipulators, one of which can be selected with respect to the conditions and the type of the manipulator. One of the methods is the closed solution which is based on the analytical expressions or forth degree or less polynomial solution in which the calculations are non-repetitive. The other method is the numerical solution. In the numerical solutions, the numbers are repeated and generally it is much slower than the closed solutions. The slowness of this method is so noticeable in such a way that principally there is no interest to use the numerical solutions to solve kinematic equations. The purpose of the present paper... 

In this paper, a new structure for the rotor of the Brushless Doubly-Fed Machine (BDFM) is introduced to reduce the machine's torque ripple. The ripple has a considerable effect on the machine start up. At the first section of the paper, analytical expressions for the air gap permeance distribution, the air gap MMF distribution, cogging torque and back EMF are presented. Then, the effects of skewing the rotor loops are analyzed. Finally, the relation between non-skewed quantities and their values in skewed coordinate are introduced  

In this paper, we employ tunneling Hamiltonian formulation to obtain analytical expression for the Josephson current in (n, m) Carbon nanotubes (CNT) sandwiched between s-wave superconductors. For metallic tubes, we find that the dominant contribution to the Josephson current arises from modes crossing the Dirac points. Contribution from such conducting channels is independent of tube diameter of carbon nanotubes. Josephson current for each CNT is determined in terms of the spacing d between the superconductors, and the angle between the tube axis and the vector normal to the interface. Averaging over orientation angles gives the Josephson current through an assembly of randomly oriented... 

In this paper, we investigate the influence of nonideal boundary conditions on the nonlinear vibration of damped Euler-Bernoulli beams subjected to harmonic loads. These nonidealities allow for small deflections and/or moments at the supports of the beam. Using the iteration perturbation method, analytical expressions for the case of simply supported beams with immovable end conditions are provided. The results reveal that the first order of approximation obtained by the proposed method is more accurate than the perturbation solutions. Moreover, compared with the previous studies, some interesting phenomenon is predicted. We have shown that in some special combinations of the nonidealities... 

In this paper, an analytical circuit model is proposed for 2-D arrays of graphene disks. First, we derive an analytical expression for the surface current density on a single graphene disk in the subwavelength regime, induced by a normally incident plane wave. The solution is then extended to 2-D arrays of graphene disks using perturbation theory. Finally, by applying appropriate boundary conditions, an R - L - C equivalent circuit of the structure is obtained. It is shown that both a single graphene disk and periodic array of graphene disks have dual capacitive-inductive nature. The results of the proposed model are in excellent agreement with those obtained by full-wave simulations  

Analytical expressions are given for zeroth-order diffraction efficiencies of metallic gratings with slanted and straight slit arrays at microwave and terahertz frequencies when the slit width is small enough to ensure that non-principal eigenmodes supported by the slit remain below cut-off. These expressions show that at lower normalized frequencies when the grating is zeroth order and all off-specular diffraction orders are evanescent, metallic slit arrays with slanted and straight walls could become identical to each other whenever certain relation is held between the geometrical parameters of the two structures. A noteworthy advantage of juxtaposing slanted and slit arrays is that it... 

In this paper, homotopy perturbation and modified Lindstedt-Poincare methods are employed for nonlinear free vibrational and buckling analysis of simply supported and double-clamped beams subjected to axial loads. Mid-plane stretching effect has also been accounted in the model. Galerkin's decomposition technique is implemented to convert the dimensionless equation of the motion to nonlinear ordinary differential equation. Homotopy and modified Lindstedt-Poincare (HPM) are applied to find analytic expressions for nonlinear natural frequencies and critical axial loads of the beams. Effects of design parameters such as axial load and slenderness ratio are investigated. The analytic expressions... 

A different approach in the calculation of two-dimensional local density of states has been presented for a two-dimensional finite rectangular-lattice photonic crystal with a separable profile of permittivity. Approximate staircase structures are already shown to be useful for their ability to reproduce actual properties of practical square lattice photonic crystals. Using the effective resonance approach in a Fabry-Perot resonator and transfer matrix method an analytical expression for calculating a two-dimensional local density of states can be derived for both polarisations in the structure. It is shown that for this geometry one can resolve the modes as a product of two separate... 

We analytically relate the giant Goos-Hanchen shift, observed at the interface of a high refractive index prism and a waveguide structure with an arbitrary refractive index profile, to the spatial resonance phenomenon. The proximity effect of the high refractive index prism on modal properties of the waveguide is discussed, and the observed shift is expressed in terms of proper and improper electromagnetic modes supported by the waveguide with no prism. The transversely increasing improper modes are shown playing an increasingly important role as the high refractive index prism comes closer to the waveguide  

We study the rotational motion of nano-flake ferromagnetic disks suspended in a Newtonian fluid, as a potential material owing the vortex-like magnetic configuration. Using analytical expressions for hydrodynamic, magnetic and Brownian torques, the stochastic angular momentum equation is determined in the dilute limit conditions under applied magnetic field. Results are compared against experimental ones and excellent agreement is observed. We also estimate the uncertainty in the orientation of the disks due to the Brownian torque when an external magnetic field aligns them. Interestingly, this uncertainty is roughly proportional to the ratio of thermal energy of fluid to the magnetic energy... 

We propose an effective medium theory for a one-dimensional periodic array of rectangular grooves covered by a graphene sheet. Parameters of the effective medium model are given by explicit analytical expressions for both major polarizations TM and TE, and for all incident angles. In extraction of this model, we assumed single mode approximation inside the grooves. The effect of non-specular diffraction orders outside the grating, as well as the plasmonic response of the graphene sheet in the far-infrared spectrum, is addressed by introducing an effective surface conductivity at the interface of the metallic grating and the ambient environment. It is shown that surface plasmons in graphene... 

A novel method to compute guided mode reflectivity from optical waveguide end-facet is presented in this paper. First, rational function fitting method (RFFM) is applied in characteristic Green’s function (CGF) technique to find an approximate closed-form analytic expression for spatial Green’s function of abruptly truncated slab waveguide. Then, derived closed-form relation along with the exact results of spatial Green’s function, obtained by full wave solution, are incorporated in an efficient optimization problem. The fast Newton reflective method with trust region algorithm are utilized for optimized reflection coefficients of guided modes. The main advantage of the proposed CGF-RFFM... 

In diffusion-based molecular communication (DMC), a transmitter nanomachine is responsible for signal modulation. Thereby, the transmitter has to be able to control the release of the signaling molecules employed for representing the transmitted information. In nature, an important class of control mechanisms for releasing molecules from cells utilizes ion channels which are pore-forming proteins across the cell membrane. The opening and closing of the ion channels is controlled by a gating parameter. In this paper, an ion channel based modulator for DMC is proposed which controls the rate of molecule release from the transmitter by modulating a gating parameter signal. Exploiting the... 

In this paper, we propose a general delay and stability performance analysis in Heterogeneous Cellular Caching Networks (HCCNs), based on queuing theory. We introduce new performance metrics in HCCNs and propose an optimization problem which minimizes the average experienced delay for users by ensuring the stability of the network. In addition, from the design perspective, we address the problem of finding the minimum cache size for the small cell base stations (SBSs) for having a tolerable average delay and also a stable network. Finally, the analytic expressions derived in this paper are validated through real trace-driven experiments on traffic of YouTube video requests  

Due to various sources of nonlinearities, micro/nano-electro-mechanical-system (MEMS/NEMS) resonators present highly nonlinear behaviors including softening- or hardening-type frequency responses, bistability, chaos, etc. The general Duffing equation with quadratic and cubic nonlinearities serves as a characterizing model for a wide class of MEMS/NEMS resonators as well as lots of other engineering and physical systems. In this paper, after brief reviewing of various sources of nonlinearities in micro/nano-resonators and discussing how they contribute to the Duffing-type nonlinearities, we propose a Homotopy Analysis Method (HAM) approach for derivation of analytical solutions for the... 

Due to various sources of nonlinearities, micro/nano-electro-mechanical-system (MEMS/NEMS) resonators present highly nonlinear behaviors including softening- or hardening-type frequency responses, bistability, chaos, etc. The general Duffing equation with quadratic and cubic nonlinearities serves as a characterizing model for a wide class of MEMS/NEMS resonators as well as lots of other engineering and physical systems. In this paper, after brief reviewing of various sources of nonlinearities in micro/nano-resonators and discussing how they contribute to the Duffing-type nonlinearities, we propose a Homotopy Analysis Method (HAM) approach for derivation of analytical solutions for the... 

A thermodynamically consistent phase field model for crack propagation is analyzed. The thermodynamic driving force for the crack propagation is derived based on the laws of thermodynamics. The Helmholtz free energy satisfies the thermodynamic equilibrium and instability conditions for the crack propagation. Analytical solutions for the Ginzburg–Landau equation including the surface profile and the estimation of the kinetic coefficient are found. It is shown how kinetic coefficient affects the local stress field. The local critical stress for the crack propagation is calibrated with the theoretical strength which gives the value of the crack surface width. The finite element method is... 

Clamp mode snubbers are very well suited for the series structure of the insulated-gate bipolar transistors (IGBTs) in pulsed power applications. They properly meet the necessities expected from them such as the fast operating of the series IGBTs since they have no effect on the gate side. In addition, they can provide safe voltage condition for the IGBTs in short circuit faults, which are very probable in pulsed applications. The clamp mode snubber can perform its voltage balancing task whenever the power capacity of the snubber can support the injected powers due to the voltage unbalancing factors. This paper initially introduces the main factors injecting power to the snubbers. Then, it... 

In the present work, an analytical solution is presented for the scattering of transverse surface waves by a homogeneous piezoelectric fiber contained in a functionally graded piezoelectric half-space with exponential variation. The boundary value problem of interest is solved by constructing an appropriate set of multipole functions which satisfy: (a) the electromechanical field equations in the half-space, (b) the boundary conditions along its free surface, and (c) the far-filed radiation conditions. It is shown that the simple poles of these functions are related to the roots of the pertinent dispersion relation. For the case of electrically short condition along the free surface of the... 

A thermodynamically consistent phase field model for crack propagation is analyzed. The thermodynamic driving force for the crack propagation is derived based on the laws of thermodynamics. The Helmholtz free energy satisfies the thermodynamic equilibrium and instability conditions for the crack propagation. Analytical solutions for the Ginzburg–Landau equation including the surface profile and the estimation of the kinetic coefficient are found. It is shown how kinetic coefficient affects the local stress field. The local critical stress for the crack propagation is calibrated with the theoretical strength which gives the value of the crack surface width. The finite element method is...