Search for: eigenvalues-and-eigenfunctions
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    New basis functions for wave equation

    , Article Scientia Iranica ; Volume 23, Issue 6 , 2016 , Pages 2928-2933 ; 10263098 (ISSN) Khorasani, S ; Sharif University of Technology
    Sharif University of Technology 
    The Differential Transfer Matrix Method is extended to the complex plane, which allows dealing with singularities at turning points. The results for real-valued systems are simplified and a pair of basis functions are found. These bases are a bit less accurate than WKB solutions but much easier to work with because of their algebraic form. Furthermore, these bases exactly satisfy the initial conditions and may go over the turning points without the divergent behavior of WKB solutions. The findings of this paper allow explicit evaluation of eigenvalues of confined modes with high precision, as demonstrated by few examples  

    A new simplified formula in prediction of the resonance velocity for multiple masses traversing a thin beam

    , Article Scientia Iranica ; Volume 23, Issue 1 , 2016 , Pages 133-141 ; 10263098 (ISSN) Afghani Khoraskani, R ; Mofid, M ; Eftekhar Azam, S ; Ebrahimzadeh Hassanabadi, M ; Sharif University of Technology
    In this article, transverse vibration of an Euler-Bernoulli beam carrying a series of traveling masses is analyzed. A semi-analytical approach based on eigenfunction expansion method is employed to achieve the dynamic response of the beam. The inertia of the traveling masses changes the fundamental period of the base beam. Therefore, a comprehensive parametric survey is required to reveal the resonance velocity of the traversing inertial loads. In order to facilitate resonance detection for engineering practitioners, a new simplified formula is proposed to approximate the resonance velocity  

    Bridged single-walled carbon nanotube-based atomic-scale mass sensors

    , Article Applied Physics A: Materials Science and Processing ; Volume 122, Issue 8 , Volume 122, Issue 8 , 2016 ; 09478396 (ISSN) Ali Akbari, H. R ; Shaat, M ; Abdelkefi, A ; Sharif University of Technology
    Springer Verlag 
    The potentials of carbon nanotubes (CNTs) as mechanical resonators for atomic-scale mass sensing are presented. To this aim, a nonlocal continuum-based model is proposed to study the dynamic behavior of bridged single-walled carbon nanotube-based mass nanosensors. The carbon nanotube (CNT) is considered as an elastic Euler–Bernoulli beam with von Kármán type geometric nonlinearity. Eringen’s nonlocal elastic field theory is utilized to model the interatomic long-range interactions within the structure of the CNT. This developed model accounts for the arbitrary position of the deposited atomic-mass. The natural frequencies and associated mode shapes are determined based on an eigenvalue... 

    Highly accurate and east convergent diffractive interface theory for fast analysis of metasurfaces

    , Article IEEE Journal of Quantum Electronics ; Volume 52, Issue 7 , 2016 ; 00189197 (ISSN) Nekuee, S. A. H ; Khavasi, A ; Akbari, M ; Sharif University of Technology
    Institute of Electrical and Electronics Engineers Inc 
    Recently, an approximate formalism [Opt. Express 23, 2764, (2015)] called diffractive interface theory has been reported for the fast analysis of the optical response of metasurfaces, subwavelength two-dimensional periodic arrays. In this method, the electromagnetic boundary conditions are derived using the susceptibility distribution of the metasurface, such that the analysis of metasurface is possible without solving any eigenvalue equation inside the grating layer. In this paper, we modify the boundary conditions to achieve more accurate results. In addition, in this paper, correct Fourier factorization rules are also applied leading to faster convergence rate. The obtained results are... 

    Eigenvalue estimation of the exponentially windowed sample covariance matrices

    , Article IEEE Transactions on Information Theory ; Volume 62, Issue 7 , 2016 , Pages 4300-4311 ; 00189448 (ISSN) Yazdian, E ; Gazor, S ; Bastani, M. H ; Sharifitabar, M ; Sharif University of Technology
    Institute of Electrical and Electronics Engineers Inc  2016
    In this paper, we consider an exponentially windowed sample covariance matrix (EWSCM) and propose an improved estimator for its eigenvalues. We use new advances in random matrix theory, which describe the limiting spectral distribution of the large dimensional doubly correlated Wishart matrices to find the support and distribution of the eigenvalues of the EWSCM. We then employ the complex integration and residue theorem to design an estimator for the eigenvalues, which satisfies the cluster separability condition, assuming that the eigenvalue multiplicities are known. We show that the proposed estimator is consistent in the asymptotic regime and has good performance in finite sample size... 

    Free vibration analysis of a beam with an intermediate sliding connection joined by a mass-spring system

    , Article JVC/Journal of Vibration and Control ; Volume 22, Issue 4 , 2016 , Pages 955-964 ; 10775463 (ISSN) Hozhabrossadati, S. M ; Aftabi Sani, A ; Mofid, M ; Sharif University of Technology
    SAGE Publications Inc  2016
    In the free vibration analysis of beams, the inclusion of an intermediate sliding connection with an attached mass-spring system has not been yet treated. The present paper studies the free vibrations of uniform Euler-Bernoulli beams with an intermediate sliding connection and joined by a mass-spring system. Two different types of beams are considered. The Type 1 is attached with a single-degree-of-freedom mass-spring system and the Type 2 is attached with a two-degree-of-freedom mass-spring system. The ends of both beams are elastically restrained against rotation and translation. First, the eigenvalue problems including differential equations and boundary conditions are introduced. Then,... 

    Continuum modelling of a circular planar array of coupled microwave oscillators

    , Article European Microwave Week 2009, EuMW 2009: Science, Progress and Quality at Radiofrequencies, Conference Proceedings - 39th European Microwave Conference, EuMC 2009, 28 September 2009 through 2 October 2009, Rome ; 2009 , Pages 1349-1352 ; 9782874870118 (ISBN) Tooni, S ; Banai, A ; Sharif University of Technology
    in this paper the phase distribution in an array of coupled oscillators arranged on a circular surface is discussed. Coupling is considered to be weak and each oscillator is coupled to its four nearest neighbours. In a continuum limit where the number of oscillators goes to infinity a theoretical formulation in polar coordinates is proposed to describe the dynamic behaviour of phases of the array elements. A Green's function for phase distribution of the array is proposed in terms of its normalized eigenfunctions. Beam steering can be done via detuning the edge oscillators. © 2009 EuMA  

    Dynamic behavior and transient stability analysis of fixed speed wind turbines

    , Article Renewable Energy ; Volume 34, Issue 12 , 2009 , Pages 2613-2624 ; 09601481 (ISSN) Rahimi, M ; Parniani, M ; Sharif University of Technology
    This paper analytically investigates the dynamic behavior of fixed speed wind turbines (FSWTs) under wind speed fluctuations and system disturbances, and identifies the nature of transient instability and system variables involved in the instability. The nature of transient instability in FSWT is not similar to synchronous generators in which the cause of instability is rotor angle instability. In this paper, the study of dynamic behavior includes modal and sensitivity analysis, dynamic behavior analysis under wind speed fluctuation, eigenvalue tracking, and using it to characterize the instability mode, and investigating possible outcomes of instability. The results of theoretical studies... 

    Robust stability analysis of distributed-order linear time-invariant systems with uncertain order weight functions and uncertain dynamic matrices

    , Article Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME ; Volume 139, Issue 12 , 2017 ; 00220434 (ISSN) Taghavian, H ; Tavazoei, M. S ; Sharif University of Technology
    Bounded-input bounded-output (BIBO) stability of distributed-order linear time-invariant (LTI) systems with uncertain order weight functions and uncertain dynamic matrices is investigated in this paper. The order weight function in these uncertain systems is assumed to be totally unknown lying between two known positive bounds. First, some properties of stability boundaries of fractional distributed-order systems with respect to location of eigenvalues of dynamic matrix are proved. Then, on the basis of these properties, it is shown that the stability boundary of distributed-order systems with the aforementioned uncertain order weight functions is located in a certain region on the complex... 

    Geometrical influence of a deposited particle on the performance of bridged carbon nanotube-based mass detectors

    , Article Physica E: Low-Dimensional Systems and Nanostructures ; Volume 94 , 2017 , Pages 31-46 ; 13869477 (ISSN) Ali Akbari, H. R ; Ceballes, S ; Abdelkefi, A ; Sharif University of Technology
    A nonlocal continuum-based model is derived to simulate the dynamic behavior of bridged carbon nanotube-based nano-scale mass detectors. The carbon nanotube (CNT) is modeled as an elastic Euler-Bernoulli beam considering von-Kármán type geometric nonlinearity. In order to achieve better accuracy in characterization of the CNTs, the geometrical properties of an attached nano-scale particle are introduced into the model by its moment of inertia with respect to the central axis of the beam. The inter-atomic long-range interactions within the structure of the CNT are incorporated into the model using Eringen's nonlocal elastic field theory. In this model, the mass can be deposited along an... 

    Deriving surface impedance for 2-d arrays of graphene patches using a variational method

    , Article IEEE Journal of Quantum Electronics ; Volume 53, Issue 1 , 2017 ; 00189197 (ISSN) Barzegar Parizi, S ; Tavakol, M. R ; Khavasi, A ; Sharif University of Technology
    In this paper, we extract the fundamental resonant mode of a graphene patch using a variational method. We use 2-D eigenvalue problem obtained from the integral equation governing the surface current on graphene patterns under quasi-static approximation. To compute the eigenvalues, we propose three trial eigenfunctions, which meet the boundary conditions. We investigate the accuracy of these eigenfunctions with comparing to the results obtained by full wave simulations. Finally, we analyze square-lattice arrangements of graphene patches using the most accurate proposed eigenfunction and derive a very accurate surface impedance for it. The proposed surface impedance is much more precise than... 

    Numerical modeling of shear band propagation in porous plastic dilatant materials by XFEM

    , Article Theoretical and Applied Fracture Mechanics ; Volume 95 , 2018 , Pages 164-176 ; 01678442 (ISSN) Mikaeili, E ; Liu, P ; Sharif University of Technology
    Elsevier B.V  2018
    This paper studies mixed-mode shear band propagation behaviors in porous plastic dilatant materials by the extended finite element method (XFEM). The Drucker-Prager elastoplastic model is combined with the strong discontinuity method to simulate the dilatant shear band. First, the dissipative nature of the localized area with displacement jump is integrated into the constitutive model by introducing a cohesive law. A new contribution lies that the yielding function is modified in the localized region to calculate the cohesive traction within the framework of the XFEM. The shear band propagation direction is determined by the singularity of the acoustic tensor and the corresponding... 

    Robust stability analysis of uncertain multiorder fractional systems: young and Jensen inequalities approach

    , Article International Journal of Robust and Nonlinear Control ; Volume 28, Issue 4 , March , 2018 , Pages 1127-1144 ; 10498923 (ISSN) Taghavian, H ; Tavazoei, M. S ; Sharif University of Technology
    John Wiley and Sons Ltd  2018
    Robust stability analysis of multiorder fractional linear time-invariant systems is studied in this paper. In the present study, first, conservative stability boundaries with respect to the eigenvalues of a dynamic matrix for this kind of systems are found by using Young and Jensen inequalities. Then, considering uncertainty on the dynamic matrix, fractional orders, and fractional derivative coefficients, some sufficient conditions are derived for the stability analysis of uncertain multiorder fractional systems. Numerical examples are presented to confirm the obtained analytical results. Copyright © 2017 John Wiley & Sons, Ltd  

    Optimal and robust waveform design for MIMO radars

    , Article 2009 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2009, Taipei, 19 April 2009 through 24 April 2009 ; 2009 , Pages 2085-2088 ; 15206149 (ISSN); 9781424423545 (ISBN) Naghibi, T ; Behnia, F ; Institute of Electrical and Electronics Engineers; Signal Processing Society ; Sharif University of Technology
    Waveform design for Target identification and classification in MIMO radar systems has been studied in several recent works. While the previous works considered signal independent noise, here we extend the results to the case where signal-dependent noise, clutter, is also present and then we find the optimum waveform for several estimators differing in the assumptions on the given statistics. Computing the optimal waveforms for MMSE estimator leads to the Semi-definite programming (SDP) problem. Finding the optimal transmit signals for CSLS estimator results in a minimax eigenvalue problem. Finally it is shown that equal power waveforms are the best transmit signals for the SLS estimator.... 

    Investigation of the transient growth in plane jet by non-modal stability analysis

    , Article Fluid Dynamics Research ; Volume 51, Issue 5 , 2019 ; 01695983 (ISSN) Gohardehi, S ; Afshin, H ; Farhanieh, B ; Sharif University of Technology
    Institute of Physics Publishing  2019
    Linear stability analysis is used to characterize the dynamics of a plane jet by incorporating non-modal stability analysis besides classical global temporal stability analysis. It is explained that similar shapes of different global modes are the result of non-normal characteristics of linearized Navier Stokes equations. Optimal initial disturbances and their eigenfunctions together with transient energy growth are obtained for different time horizons and Reynolds numbers of the jet in the linear unstable configuration. These structures are localized at the upstream of the jet nozzle at the boundary layer. The transient growth of the inlet perturbation in limited time bounds is found in the... 

    Effect of unitary transformation on Bayesian information criterion for source numbering in array processing

    , Article IET Signal Processing ; Volume 13, Issue 7 , 2019 , Pages 670-678 ; 17519675 (ISSN) Johnny, M ; Aref, M. R ; Razzazi, F ; Sharif University of Technology
    Institution of Engineering and Technology  2019
    An approach based on unitary transformation for the problem of estimating the number of signals is proposed in this study. Among the information theoretic criteria, the authors focus on the conventional Bayesian information criterion (BIC) in the presence of a uniform linear array. The sample covariance matrix of this array is transformed into the real symmetric one by using a unitary transformation. This real symmetric matrix has real eigenvalues and eigenvectors. Therefore its eigenvalue decomposition needs only real computations. Since the eigenvalues of this real symmetric matrix are equal to the eigenvalues of the sample covariance matrix, by replacing them in BIC formula, the term... 

    Linear spatial stability analysis of particle-laden stratified shear layers

    , Article Journal of the Brazilian Society of Mechanical Sciences and Engineering ; Volume 41, Issue 6 , 2019 ; 16785878 (ISSN) Khavasi, E ; Firoozabadi, B ; Sharif University of Technology
    Springer Verlag  2019
    Hydrodynamic instabilities at the interface of stratified shear layers could occur in various modes. These instabilities have an important role in the mixing process. In this work, the linear stability analysis in spatial framework is used to study the stability characteristics of a particle-laden stratified two-layer flow. The effect of parameters such as velocity-to-density thickness ratio, bed slope, viscosity as well as particle size on the stability is considered. A simple iterative method applying the pseudospectral collocation method that employed Chebyshev polynomials is used to solve two coupled eigenvalue equations. Based on the results, the flow becomes stable for Richardson... 

    UWB orthogonal pulse design using Sturm–Liouville boundary value problem

    , Article Signal Processing ; Volume 159 , 2019 , Pages 147-158 ; 01651684 (ISSN) Amini, A ; Mohajerin Esfahani, P ; Ghavami, M ; Marvasti, F ; Sharif University of Technology
    Elsevier B.V  2019
    The problem of designing UWB pulses which meet specific spectrum requirements is usually treated by filtering common pulses such as Gaussian doublets, modified Hermite polynomials and wavelets. When there is the need to have a number of orthogonal pulses (e.g., in a multiuser scenario), a naive approach is to filter all the members of an orthogonal set, which is likely to destroy their orthogonality property. In this paper, we study the design of a set of pulses that simultaneously satisfy the orthogonality property and spectrum requirements. Our design is based on the eigenfunctions of Sturm–Liouville boundary value problems. Indeed, we introduce Sturm–Liouville differential equations for... 

    Mimicking the Hadamard discrete-time quantum walk with a time-independent Hamiltonian

    , Article Quantum Information Processing ; Volume 18, Issue 5 , 2019 ; 15700755 (ISSN) Khatibi Moqadam, J ; de Oliveira, M. C ; Sharif University of Technology
    Springer New York LLC  2019
    The discrete-time quantum walk dynamics can be generated by a time-dependent Hamiltonian, repeatedly switching between the coin and the shift generators. We change the model and consider the case where the Hamiltonian is time-independent, including both the coin and the shift terms in all times. The eigenvalues and the related Bloch vectors for the time-independent Hamiltonian are then compared with the corresponding quantities for the effective Hamiltonian generating the quantum walk dynamics. Restricted to the non-localized initial quantum walk states, we optimize the parameters in the time-independent Hamiltonian such that it generates a dynamics similar to the Hadamard quantum walk. We... 

    Sensitivity-based generators redispatch to improve electromechanical mode damping considering transmission lines resistance

    , Article 27th Iranian Conference on Electrical Engineering, ICEE 2019, 30 April 2019 through 2 May 2019 ; 2019 , Pages 491-496 ; 9781728115085 (ISBN) Setareh, M ; Parniani, M ; Sharif University of Technology
    Institute of Electrical and Electronics Engineers Inc  2019
    This paper proposes a novel formula to calculate sensitivities of electromechanical modes to generators active power changes. Quadratic eigenvalue problem is applied to construct the framework of the proposed formula. Sensitivity factors are calculated using power system model parameters and power flow variables, which can be either obtained via state estimation or measured directly by phasor measurement units. The 39-bus New England power system is used to verify performance of the proposed method