Sharif Digital Repository

Li's Fourier factorization rule [J. Opt. Soc. Am. A 13, 1870 (1996)] was recently shown to be problematic to apply to highly conducting metallic gratings. We provide further information about the applicability of different differential methods and are concerned with the relation of observed numerical artifacts, the total number of retained space harmonics, the presence of both positive and negative permittivity inside the groove region, and the validity of Li's inverse rule. Two different cases corresponding to lossless and low-loss binary metallic gratings are considered, and it is shown that an increase in the number of retained space harmonics can relieve the presence of numerical... 

The present paper addresses an analytical method to determine the overall behavior of piezocomposite materials containing body centered cubic (BCC) distribution of arbitrary oriented ellipsoidal heterogeneities. This approach is based on the extension of the electromechanical equivalent inclusion method (EMEIM) to interacting multi-inhomogeneities. In this treatment the short and long range interactions of the piezoelectric particles are appropriately incorporated through the homogenizing eigenstrainelectric field. The periodicity of the microstructure of the medium suggests representing the eigenfields in terms of Fourier series, accounting for the matrixparticle, interparticle and... 

This paper studies the subject of adaptive noise cancelation using the Kalman filtering technique to achieve high precision and fast convergence. It is shown that the Kalman filter can successfully be designed to detect and extract periodic noises which may be constituted of different sinusoidal components with possibly unknown and/or time-varying frequencies. This highlights the feature of Kalman filter in synthesizing periodic noises in the time-domain which is not possible using Fourier-based methods such as DFT. Usefulness of the method is discussed in the context of two examples: active cancelation of periodic noises from audio waveforms and filtering of electrocardiogram measurements.... 

In this work the Fourier series and Zakian and Schapery methods are considered to numerically solve the Laplace transform of a pressure distribution equation for radial flow and to generate the type curves for three different boundary conditions. The results show that the Schapery method leads to approximate solutions for small values of dimensionless time. For large values, however, this method is almost accurate and hence is recommended because it is fast to apply compared to other algorithms. It has been found that the accuracy of the Schapery method for early time prediction can be improved to almost a perfect match with analytical results through multiplying the Schapery relation by a... 

The resonance frequencies of cantilever carbon nanocones (CNCs) up to 4 nm in height are determined using molecular dynamics simulation based on adaptive intermolecular reactive empirical bond order potential. The frequency content of the free vibrations of CNCs under a lateral initial excitation at the tip is analyzed using fast Fourier transformation, and the resonance frequencies are obtained. The results are reported for various samples to investigate the dependency of the resonance frequency to the geometrical parameters and temperature of CNCs  

This study pertains to the free vibration problem of beams on an elastic foundation of the Winkler type, which is distributed over a particular length of the beam. Closed form solutions are developed by solving the governing differential equations of beams. Moreover, an innovative mathematical approach is proposed to find the precise analytical solution of the free vibration of beams with mixed boundary conditions. Results are discussed in detail through verification studies. Ultimately, it was concluded that the proposed mathematical method could successfully obtain the exact solution to the free vibration problem of beams on partial elastic foundations under mixed boundary conditions  

This paper deals with estimation of fractional order and pole locator in fractional order systems. The estimation is based on Bode diagram of the system that is obtained using input and output measurements. Here the magnitude diagram is approximated with number of straight lines depending on the level of complexity and in consequence a very good estimation of fractional order and acceptable approximations of pole locators are determined. Relying on the proposed method, complexity of fractional order system identification which is mostly due to the estimation of fractional order is substantially resolved. Some example simulation results are provided to explain the work and show its... 

In this paper, we have developed an efficient method for obtaining an orthonormal wavelet that is matched to a given signal. The error between the wavelet and the given signal is minimized subject to the constraints of the amplitude and phase of the band-limited wavelet spectrum. To consider the constraints of the minimization problem, the Lagrange multipliers technique is applied. Variational method reduced the optimal matching problem to the solution of a set of functional equations for the amplitude and phase of the wavelet spectrum. Continuous functional equations were written in terms of Fourier coefficients of the phase of the transfer function of the quadrature low pass filter at the... 

Noise reduction and signal decomposition are among important and practical issues in time-domain signal analysis. This paper presents an adaptive notch filter (ANF) to achieve both these objectives. For noise reduction purpose, the proposed adaptive filter successfully extracts a single sinusoid of a possibly time-varying nature from a noise-corrupted signal. The paper proceeds with introducing a chain of filters which is capable of estimating the fundamental frequency of a signal composed of harmonically related sinusoids, and of decomposing it into its constituent components. The order of differential equations governing this algorithm is 2n + 1, where n is the number of constituent... 

Spectral reconstructions provide rigorous means to remove the Gibbs phenomenon and accelerate the convergence of spectral solutions in non-smooth differential equations. In this paper, we show the concurrent emergence of truncated convolution errors could entirely disrupt the performance of most reconstruction techniques in the vicinity of discontinuities. These errors arise when the Fourier coefficients of the product of two discontinuous functions, namely f=gh, are approximated via truncated convolution of the corresponding Fourier series, i.e. fˆk≈∑|ℓ|⩽Ngˆℓhˆk−ℓ. Nonetheless, we numerically illustrate and rigorously prove that the classical Gegenbauer method remains exceptionally robust... 

This paper presents a digital hardware implementation of a frequency adaptive Hopf oscillator along with investigation on systematic behavior when they are coupled in a population. The mathematical models of the oscillator are introduced and compared in sense of dynamical behavior by using system-level simulations based on which a piecewise-linear model is developed. It is shown that the model is capable to be implemented digitally with high efficiency. Behavior of the oscillators in different network structures to be used for dynamic Fourier analysis is studied and a structure with more precise operation which is also more efficient for FPGA-based implementation is implemented. Conceptual... 

Li's Fourier factorization rules [J. Opt. Soc. Am. A 13, 1870 (1996)] should be applied to achieve a fast convergence rate in the analysis of diffraction gratings with the Fourier modal method. I show, however, that Li's inverse rule cannot be applied for periodic patterns of graphene when the conventional boundary condition is used. I derive an approximate boundary condition in which a nonzero but sufficiently small height is assumed for the boundary. The proposed boundary condition enables us to apply the inverse rule, leading to a significantly improved convergence rate. A periodic array of graphene ribbons is in fact a special type of finite-conductivity strip grating, and thus the... 

Boundary-layer effects in lengthy cross-ply laminated circular cylindrical shell panels under uniform axial extension are investigated by two analytical solutions. First, Reddy's layerwise theory with state-space approach is utilized to determine the local interlaminar stresses. In this method, the general displacement field is discretized through the shell thickness by a linear shape function. When the shell panel is subjected to an axial force, the axial strain is estimated by an equivalent single-layer theory. Second, the stress-function approach along with Fourier series expansion is applied to develop a novel elasticity solution. The elasticity solution, which is based on simply-support... 

Despite numerous experimental and numerical studies, fundamental understanding of how the matrix block height, the density difference between petroleum and gas, and matrix capillary pressure could affect the oil recovery from a single matrix block in naturally fractured reservoirs remains a topic of debate in the literature. In this work a one-dimensional gravity drainage model developed by Firoozabadi and Ishimoto (1994) is considered and numerically solved. The Fourier series method is applied for a numerical Laplace inversion of the dimensionless mathematical model; this type of inversion method has rarely been used in petroleum applications. The obtained results revealed that by... 

Chitosan/bacterial cellulose composite films containing diamond nanoparticles (NDs) with potential application as wound dressing are introduced. Microstructural studies show that NDs are uniformly dispersed in the matrix, although slight agglomeration at concentrations above 2 wt % is seen. Fourier transform infrared spectroscopy reveals formation of hydrogen bonds between NDs and the polymer matrix. X-ray diffraction analysis indicates reduced crystallinity of the polymer matrix in the presence of NDs. Approximately 3.5-fold increase in the elastic modulus of the composite film is obtained by the addition of 2 wt % NDs. The results of colorimetric analysis show that the composite films are... 

The accuracy of Photoplethysmographic signals is often not adequate due to motional artifacts induced in the recording site. Over recent decades there has been a widespread effort to reduce these artifacts and different methods are used for this aim. Nevertheless there are still some contradictory results reported by different methods about their effectiveness in artifact reduction. In this paper, we aim to compare three of established methods for PPG noise reduction on a unique dataset. Among different reported methods, we have chosen Adaptive Noise Cancellation (ANC), Discrete Wavelet Transform (DWT) and a newly developed method Cycle-by-cycle Fourier Series Analysis (CFSA) for denoising.... 

In this paper, the steady-state stresses in a homogeneous isotropic half-space under a moving wheel-type load with constant subsonic speed, prescribed on a finite patch on the boundary, are investigated. Navier's equations of motion in 2D case were modified via Stokes-Helmholtz resolution to a system of partial differential equations. A double Fourier-Laplace transformation procedure was employed to solve the system of partial differential equations in a new moving reference system, regarding the boundary conditions. The effects of force transmission from the contact patch to the half-space have been considered in the boundary conditions. Utilizing a property of Laplace transformation leads... 

Numerical modeling of periodically patterned graphene sheets (PPGS) embedded in planar multilayered media using Fourier-based methods suffers from very slow convergence because of the fact that the conductivity is zero in unfilled areas of the patterned surface and, thus, the so-called Li's inverse rule is not applicable. In this paper, a simple and efficient approach is proposed to overcome this problem such that the exact boundary condition can be applied and the surface current density on PPGS can be obtained accurately. Here, the PPGS is modeled as a conductive surface and only its conductivity representation by the Fourier series is modified. The proposed method can be used easily for... 

Flight dynamics of the guided vehicle is modelled by the aid of linear and angular equations of motions using Lagrange's approach in this paper. Governing equations of the control system and the elastic behavior of the vehicle are added to the equations of dynamic states. Flexibility effect is modelled using the normal modes, generalized coordinates and forces. For validation of modified FORTRAN simulation code, the stability of specific vehicles is determined and compared with the same results in the literature. Using this code and by solving the governing equations for the desired flight vehicle, the aeroservoelasticity is analyzed and then the results are compared with the rigid cases and...