Sharif Digital Repository

Oscillatory condition in LTI dynamic systems is generally expressed as possessing purely imaginary solutions by their characteristic equations. Dealing with the class of fractional order systems, such a condition is equivalently restated as owing complex roots with specific arguments by a polynomial defined based on the system characteristic equation. The degree of this polynomial can be unboundedly high. Consequently, such statement for the oscillatory condition in fractional order systems, which is based on arguments of the roots of a polynomial with an unbounded degree, cannot be viewed as a closed-form expression. To tackle this challenge, this brief introduces an approach to obtain a... 

In this paper a closed-form expression is introduced to calculate slot shape of long slot leaky wave waveguide antennas at its fundamental mode of operation with minimum side lobe level (SLL). The derived equation is a function of geometrical parameters of the structure. This is an advantage because they show a clear relationship between geometrical parameters of the antenna and radiated field that allows intelligent modification of the pattern. The Gaussian slot is used to obtain the best radiation pattern with lowest SLL. The results obtained by introduced formula are compared with the full wave commercial simulator such as HFSS software which confirms the accuracy of the introduced... 

In this paper, a new procedure is developed for the solution of a general two-dimensional uncoupled symmetric double contact problem with smooth contact zones in which the indenter geometry is described by a piecewise biquadratic function. This procedure gives an approximate closed-form solution for any smooth indenter profile. In order to evaluate the accuracy of this approach, it is applied to the symmetric indentation of a flat surface by two rigidly interconnected parabolic indenters and results are compared with the exact unclosed-form solution. Moreover, this procedure is applied to the symmetric indentation of a flat surface by two rigidly interconnected cylinders to compare the... 

This paper aims to present an explicit relation for thermoelastic damping in nanobeams capturing the small-scale effects on both the continuum mechanics and heat conduction domains. To incorporate small-scale effects, the coupled equations of motion and heat conduction are obtained by employing the nonlocal elasticity theory and the dual-phase-lag heat conduction model. Adopting simple harmonic forms for transverse deflection and temperature increment and solving the governing equations, real and imaginary parts of the frequency are extracted. According to the complex frequency approach, a closed-form size-dependent expression for evaluating thermoelastic damping in nanobeams is derived. To... 

A novel and general formulation for wave propagation in time-varying media is presented. Unlike previousreports, our formalism is able to solve propagation in media with arbitrary time variations of permittivity orpermeability, for both transient and steady-state periodic variations. The formulation is approximate yet strikingly accurate in most practical cases. The provided closed-form expressions show that the normalized averagepower after the transition of the permittivity does not depend on the details of the transition, while the energydensity does. Some important discussions are made about time-periodic media, and it is shown that there is anaccumulation of energy when the temporal... 

In this paper, collision of two balls in three dimensions with regard to energy loss and friction is studied. This investigation intends to propose the procedure which can determine the condition of pure sliding, sliding with rolling or sticking, and rolling or sticking at the beginning of contact. Furthermore, the other aim of this research is to suggest the closed-form relation for post-collision angular and linear velocities in which the possibility of three regimes of impact, pure sliding, sliding with rolling, and pure rolling, are considered. In this investigation, viscous Hertz contact force describes the normal interaction force. Moreover, stick regime is not taken into account and... 

Feed-forward is one of the main methods for linearising microwave power amplifiers. The level of inter-modulation rejection (IMR) values can be predicted by appropriate modelling of the feed-forward microwave amplifier. Here, we have presented closed form expressions, which can be used for predicting the IMR for the first and second adjacent channels. Fifth- and third-order nonlinear models have been used for the main and error amplifiers, respectively. The predicted values have been verified using ADS simulator and a MATLAB program. © The Institution of Engineering and Technology 2007  

In this paper, we will address the issue of power distribution and decoding order in the uplink side of a multirate code division multiple access (CDMA) system based on linear successive interference cancellation (SIC). First, the closed form expressions for the required received powers at the base station, in order to achieve the users bit rate and Quality of Service (QoS) requirements, will be derived. Then, we will investigate the problem of optimal decoding order of the users under imperfect interference cancellation condition and will show that optimum decoding order of users, unlike the case of perfect SIC, is a function of their requested SINR values in addition to their path gains.... 

In this article, an analytical method for calculating pull-in voltage is proposed. This method can accurately predict pull-in voltage of clamped-free, clamped-clamped and curved micro- and nano-beams. In this study, mid-plane stretching, axial stress, initial deformation and the effect of size are taken into account. To achieve this goal, governing equation of beam based on modified couple stress theory was first derived and then transformed to a single degree of freedom (D.O.F) model by Galerkin method. In this model, electrostatic force appears in integral form which is approximated to non-integral form employing Genetic Algorithm. This single degree of freedom model provides means for... 

In this paper, the dynamic characteristics of skewed bridges are explored analytically. Closed form solutions for translational and torsional periods of free vibration and mode shapes are given for slab-girder skewed bridges. Moreover, the seismic displacement of the deck of skewed bridges is calculated using the response spectrum method and its skew term is compared with the requirement of AASHTO. The effects of seismic force resisting elements, such as elastomeric bearings and end diaphragms are included. It is shown that the skew term in AASHTO's equation can underestimate the seat width requirement for some bridges. A new skew term for the bridge seat width requirement is suggested  

Non-linear bending analysis of tapered functionally graded (FG) beam subjected to thermal and mechanical load with general boundary condition is studied. The governing equations are derived and a discussion is made about the possibility of obtaining analytical solution. In the case of no axial force along the beam, a closed form solution is presented for the problem. For the general case with axial force, the Galerkin technique is employed to overcome the shortcoming of the analytical solution. Moreover, the Generalized Differential Quadrature (GDQ) method is also implemented to discretize and solve the governing equations in the general form and validate the results obtained from two other... 

A closed-form spatial Green's function for finite dielectric structures is derived by using a combination of the characteristic Green's function (CGF) and rational function fitting method (RFFM). CGF-RFFM represents both of the discrete and continuous spectrum contributions efficiently by using the modified VECTFIT algorithm. To obtain more accurate results, reflection coefficient correction due to the surface waves (SWs) incident on the the end-facet is considered. The main advantage of this method lies in its speed as well as accuracy. Excellent agreements with the rigorous method of moments (MoM) are shown in several examples  

In this paper, we investigate the diversity-multiplexing tradeoff (DMT) for multi-relay channels in finite-SNR regime. In our analysis, we consider the decode and forward (DF) relaying strategy and a line of sight path from source to destination. First, we determine the outage probability in a multi-relay scenario and obtain its exact analytical expressions. Then, the outage probability of a multi-relay channel with relay selection is calculated and provided as a closed-form expression. Based on these results, we determine the DMT in finite-SNR regime. Finally, using simulation results, we show that our analysis has accurate results which coincides with that of obtained from Monte-Carlo... 

MIMO radar is the next generation radar which transmits arbitrary waveforms at each one of its apertures. It has been shown that the design of waveforms for MIMO radars in order to synthesize a desired spatial beampattern is mapped into a waveform correlation matrix R design in the narrowband case. As of now, given a desired beampattern or estimated locations information of targets, calculating R has been modeled as an optimization problem like semi-definite programming. Also, in some special cases like rectangular beampattern, closed-form solutions for R has been proposed. In this paper, we introduce a fast algorithm which is capable of designing R in order to achieve more arbitrary... 

In this paper, two circuit models are proposed for analytical investigation of extraordinary transmission through periodic array of subwavelength stepped slits in a thick metallic plate. A cascade model is first developed and then a stub model is suggested for cases that the cascade model is not accurate. The parameters of the proposed circuits are given by closed-form expressions. Both symmetric and asymmetric stepped slits are considered  

In this work an analytical solution is presented for a viscoelastic micro-beam based on the modified couple stress theory which is a non-classical theory in continuum mechanics. The modified couple stress theory has the ability to consider small size effects in micro-structures. It is strongly emphasized that without considering these effects in such structures the solution will be wrong and not suitable for designing systems in micro-scales. In this study correspondence principle is used for deriving constitutive equations for viscoelastic material based on the modified couple stress theory. Governing equilibrium equations are obtained by considering an element of micro-beam. Closedform... 

We present a formulation for the nonlinear optical response in gapped graphene, where the low-energy single-particle spectrum is modeled by massive Dirac theory. As a representative example of the formulation presented here, we obtain a closed form formula for the third harmonic generation in gapped graphene. It turns out that the covariant form of the low-energy theory gives rise to peculiar logarithmic singularities in the nonlinear optical spectra. The universal functional dependence of the response function on dimensionless quantities indicates that the optical nonlinearity can be largely enhanced by tuning the gap to smaller values  

A circuit model is proposed for periodic 1-D array of metallic strips in the sub-wavelength regime. The parameters of the proposed circuit and their dependence on frequency are all explicitly given by closed form expressions. The necessity of using numerical simulation to extract model parameters is thus sidestepped. It is demonstrated that the proposed model is valid at different incident angles and for arbitrary surrounding mediums given that there is only one propagating diffracted order outside the grating and only one guided mode supported by the slits. Both major polarizations are studied in this paper  

By reformulating the governing equations of the first-order theory into those describing the interior and edge-zone problems of the plate, closed-form solutions are presented for analysis of functionally graded circular sector plates with vertex angle (Formula presented.) whose radial edges are simply supported and subjected to transverse loading and heat conduction through the plate thickness. Various types of clamped, simply supported, and free-edge boundary supports are considered on the circular edge of the plate. The material properties are graded through the plate thickness according to a power-law distribution of the volume fraction of the constituents. The effects of material... 

This paper deals with learning an overcomplete set of atoms that have low mutual coherence. To this aim, we propose a new dictionary learning (DL) problem that enables a control on the amounts of the decomposition error and the mutual coherence of the atoms of the dictionary. Unlike existing methods, our new problem directly incorporates the mutual coherence term into the usual DL problem as a regularizer. We also propose an efficient algorithm to solve the new problem. Our new algorithm uses block coordinate descent, and updates the dictionary atom-by-atom, leading to closed-form solutions. We demonstrate the superiority of our new method over existing approaches in learning low-coherence...