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eigenvalues-and-eigenfunctions
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New sufficient conditions for robust stability analysis of interval matrices
, Article Systems and Control Letters ; Volume 61, Issue 12 , 2012 , Pages 1117-1123 ; 01676911 (ISSN) ; Babazadeh, M ; Karimi, H ; Nobakhti, A ; Sharif University of Technology
2012
Abstract
This letter presents new sufficient conditions for robust Hurwitz stability of interval matrices. The proposed conditions are based on two approaches: (i) finding a common Lyapunov matrix for the interval family and (ii) converting the robust stability problem into a robust non-singularity problem using Kronecker operations. The main contribution of the letter is to derive accurate and computationally simple optimal estimates of the robustness margin and spectral bound of general interval matrices. The evaluation of the condition relies on the solutions of linear matrix inequalities (LMIs) and eigenvalue problems, both of which are solved very efficiently. The improvements gained by using...
New basis functions for wave equation
, Article Scientia Iranica ; Volume 23, Issue 6 , 2016 , Pages 2928-2933 ; 10263098 (ISSN) ; Sharif University of Technology
Sharif University of Technology
Abstract
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
Neutron noise simulation by GFEM and unstructured triangle elements
, Article Nuclear Engineering and Design ; Volume 253 , 2012 , Pages 238-258 ; 00295493 (ISSN) ; Vosoughi, N ; Sharif University of Technology
2012
Abstract
In the present study, the neutron noise, i.e. The stationary fluctuation of the neutron flux around its mean value, is calculated in 2-group forward and adjoint diffusion theory for both hexagonal and rectangular reactor cores. To this end, the static neutron calculation is performed at the first stage. The spatial discretization of equations is based on linear approximation of Galerkin Finite Element Method (GFEM) using unstructured triangle elements. Using power iteration method, forward and adjoint fluxes with the corresponding eigenvalues are obtained. The results are then benchmarked against the valid results for BIBLIS-2D and IAEA-2D benchmark problems and DONJON computer code. The...
Multiple antenna spectrum sensing in cognitive radios
, Article IEEE Transactions on Wireless Communications ; Volume 9, Issue 2 , 2010 , Pages 814-823 ; 15361276 (ISSN) ; Nasiri-Kenari, M ; Gazor, S ; Sharif University of Technology
2010
Abstract
In this paper, we consider the problem of spectrum sensing by using multiple antenna in cognitive radios when the noise and the primary user signal are assumed as independent complex zero-mean Gaussian random signals. The optimal multiple antenna spectrum sensing detector needs to know the channel gains, noise variance, and primary user signal variance. In practice some or all of these parameters may be unknown, so we derive the Generalized Likelihood Ratio (GLR) detectors under these circumstances. The proposed GLR detector, in which all the parameters are unknown, is a blind and invariant detector with a low computational complexity. We also analytically compute the missed detection and...
Multi-objective robust design optimization (MORDO) of an aeroelastic high-aspect-ratio wing
, Article Journal of the Brazilian Society of Mechanical Sciences and Engineering ; Volume 42, Issue 11 , 2020 ; Roudbari, A ; Hajipourzadeh, P ; Sharif University of Technology
Springer Science and Business Media Deutschland GmbH
2020
Abstract
In this paper, a new approach for multi-objective robust optimization of flutter velocity and maximum displacement of the wing tip are investigated. The wing is under the influence of bending–torsion coupling and its design variables have different levels of uncertainty. In designing and optimizing wings with a high aspect ratio, the optimization process can be done in such a way to increase the flutter velocity, but this can increase the amplitude of the wing tip displacement to a point that leads to the wings damage and structural failure. Therefore, single-objective design optimization may lead to infeasible designs. Thus, for multi-objective optimization, modeling is based on the...
Multichannel electrocardiogram decomposition using periodic component analysis
, Article IEEE Transactions on Biomedical Engineering ; Volume 55, Issue 8 , August , 2008 , Pages 1935-1940 ; 00189294 (ISSN) ; Jutten, C ; Shamsollahi, M. B ; Sharif University of Technology
2008
Abstract
In this letter, we propose the application of the generalized eigenvalue decomposition for the decomposition of multichannel electrocardiogram (ECG) recordings. The proposed method uses a modified version of a previously presented measure of periodicity and a phase-wrapping of the RR-interval, for extracting the "most periodic" linear mixtures of a recorded dataset. It is shown that the method is an improved extension of conventional source separation techniques, specifically customized for ECG signals. The method is therefore of special interest for the decomposition and compression of multichannel ECG, and for the removal of maternal ECG artifacts from fetal ECG recordings. © 2006 IEEE
MR artifact reduction in the simultaneous acquisition of EEG and fMRI of epileptic patients
, Article 16th European Signal Processing Conference, EUSIPCO 2008, Lausanne, 25 August 2008 through 29 August 2008 ; 2008 ; 22195491 (ISSN) ; Sameni, R ; Jutten, C ; Hossein Zadeh, G. A ; Soltanian Zadeh, H ; Sharif University of Technology
2008
Abstract
Integrating high spatial resolution of functional magnetic resonance imaging (fMRI) and high temporal resolution of electroencephalogram (EEG) is promising in simultaneous EEG and fMRI analysis, especially for epileptic patients. The EEG recorded inside an MR scanner is interfered with MR artifacts. In this article, we propose new artifact reduction approaches and compare them with the conventional artifact reduction methods. Our proposed approaches are based on generalized eigenvalue decomposition (GEVD) and median filtering. The proposed methods are applied on experimental simultaneous EEG and fMRI recordings of an epileptic patient. The results show significant improvement over...
Modal analysis of the dynamic response of Timoshenko beam under moving mass
, Article Scientia Iranica ; Volume 22, Issue 2 , 2015 , Pages 331-344 ; 10263098 (ISSN) ; Mofid, M ; Ghannadiasl, A ; Sharif University of Technology
Sharif University of Technology
2015
Abstract
In this study, the dynamic response of a Timoshenko beam under moving mass is investigated. To this end, vectorial form orthogonality property of the Timoshenko beam free vibration modes is applied to the EEM (Eigenfunction Expansion Method). The implication of the vectorial form series and an appropriate inner product of mode shapes in combination are focused for a beam with arbitrary boundary conditions. Consequently, significant simplifications and efficacy in the utilization of the EEM in eliminating the spatial domain is achieved. In order to comprise validation, the present study is compared with the DET (Discrete Element Technique) and the RKPM (Reproducing Kernel Particle Method)
MIMO radar beamforming using orthogonal decomposition of correlation matrix
, Article Circuits, Systems, and Signal Processing ; Volume 32, Issue 4 , 2013 , Pages 1791-1809 ; 0278081X (ISSN) ; Behnia, F ; Sharif University of Technology
2013
Abstract
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...
Mimicking the Hadamard discrete-time quantum walk with a time-independent Hamiltonian
, Article Quantum Information Processing ; Volume 18, Issue 5 , 2019 ; 15700755 (ISSN) ; de Oliveira, M. C ; Sharif University of Technology
Springer New York LLC
2019
Abstract
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...
Magneto-mechanical stability of axially functionally graded supported nanotubes
, Article Materials Research Express ; Volume 6, Issue 12 , 2019 ; 20531591 (ISSN) ; Mirtalebi, H ; Ahmadian, M. T ; Sharif University of Technology
Institute of Physics Publishing
2019
Abstract
In this paper, size-dependent vibration analysis of axially functionally graded (AFG) supported nanotubes conveying nanoflow under longitudinal magnetic fields are performed, aiming at performance improvement of fluid-interaction nanosystems. Either the density or the elastic modulus of the AFG nanotube varies linearly or exponentially along the axial direction. Based on the nonlocal continuum theory, the higher-order dynamical equation of motion of the system is derived considering no-slip boundary condition. Galerkin discretization technique and eigenvalue analysis are implemented to solve the modeled equation. The validity of the simplified model is justified by comparing the results with...
Magneto-mechanical stability of axially functionally graded supported nanotubes
, Article Materials Research Express ; Volume 6, Issue 12 , 2019 ; 20531591 (ISSN) ; Mirtalebi, H ; Ahmadian, M. T ; Sharif University of Technology
Institute of Physics Publishing
2019
Abstract
In this paper, size-dependent vibration analysis of axially functionally graded (AFG) supported nanotubes conveying nanoflow under longitudinal magnetic fields are performed, aiming at performance improvement of fluid-interaction nanosystems. Either the density or the elastic modulus of the AFG nanotube varies linearly or exponentially along the axial direction. Based on the nonlocal continuum theory, the higher-order dynamical equation of motion of the system is derived considering no-slip boundary condition. Galerkin discretization technique and eigenvalue analysis are implemented to solve the modeled equation. The validity of the simplified model is justified by comparing the results with...
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) ; Firoozabadi, B ; Sharif University of Technology
Springer Verlag
2019
Abstract
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...
Linearization error in synchronization of Kuramoto oscillators
, Article Applied Mathematics and Computation ; Volume 411 , December , 2021 ; 00963003 (ISSN) ; Baharifard, F ; Hesaam, B ; Zarei, M ; Sarbazi Azad, H ; Sharif University of Technology
Elsevier Inc
2021
Abstract
Synchronization among a set of networked nodes has attracted much attention in different fields. This paper thoroughly investigates linear formulation of the Kuramoto model, with and without frustration, for an arbitrarily weighted undirected network where all nodes may have different intrinsic frequencies. We develop a mathematical framework to estimate errors of the linear approximation for globally and locally coupled networks. We mathematically prove that the eigenvector corresponding to the largest eigenvalue of the network's Laplacian matrix is enough for examining synchrony alignment and that the functionality of this vector depends on the corresponding eigenvalue. Moreover, we prove...
Linear analysis of the stability of particle-laden stratified shear layers
, Article Canadian Journal of Physics ; Vol. 92, issue. 2 , 2014 , pp. 103-115 ; ISSN: 00084204 ; Firoozabadi, B ; Afshin, H
Abstract
Hydrodynamic instabilities at the interface of stratified shear layers could occur in various modes and have an important role in the mixing process. In this work, the linear stability analysis in the temporal framework is used to study the stability characteristics of a particle-laden stratified two-layer flow for two different background density profiles: smooth (hyperbolic tangent) and piecewise linear. The effect of parameters, such as bed slope, viscosity, and particle size, on the stability is also considered. The pseudospectral collocation method employing Chebyshev polynomials is used to solve two coupled eigenvalue equations. Based on the results, there are some differences in the...
Limiting spectral distribution of the sample covariance matrix of the windowed array data
, Article Eurasip Journal on Advances in Signal Processing ; Volume 2013, Issue 1 , 2013 ; 16876172 (ISSN) ; Gazor, S ; Bastani, M. H ; Sharif University of Technology
2013
Abstract
In this article, we investigate the limiting spectral distribution of the sample covariance matrix (SCM) of weighted/windowed complex data. We use recent advances in random matrix theory and describe the distribution of eigenvalues of the doubly correlated Wishart matrices. We obtain an approximation for the spectral distribution of the SCM obtained from windowed data. We also determine a condition on the coefficients of the window, under which the fragmentation of the support of noise eigenvalues can be avoided, in the noise-only data case. For the commonly used exponential window, we derive an explicit expression for the l.s.d of the noise-only data. In addition, we present a method to...
Laplacian eigenvalue distribution and graph parameters
, Article Linear Algebra and Its Applications ; Volume 632 , 2022 , Pages 1-14 ; 00243795 (ISSN) ; Akbari, S ; Fakharan, M. H ; Trevisan, V ; Sharif University of Technology
Elsevier Inc
2022
Abstract
Let G be a graph and I be an interval. In this paper, we present bounds for the number mGI of Laplacian eigenvalues in I in terms of structural parameters of G. In particular, we show that mG(n−α(G),n]≤n−α(G) and mG(n−d(G)+3,n]≤n−d(G)−1, where α(G) and d(G) denote the independence number and the diameter of G, respectively. Also, we characterize bipartite graphs that satisfy mG[0,1)=α(G). Further, in the case of triangle-free or quadrangle-free, we prove that mG(n−1,n]≤1. © 2021 Elsevier Inc
Joint, partially-joint, and individual independent component analysis in multi-subject fMRI data
, Article IEEE Transactions on Biomedical Engineering ; Volume 67, Issue 7 , 2020 , Pages 1969-1981 ; Shamsollahi, M. B ; Sharif University of Technology
IEEE Computer Society
2020
Abstract
Objective: Joint analysis of multi-subject brain imaging datasets has wide applications in biomedical engineering. In these datasets, some sources belong to all subjects (joint), a subset of subjects (partially-joint), or a single subject (individual). In this paper, this source model is referred to as joint/partially-joint/individual multiple datasets unidimensional (JpJI-MDU), and accordingly, a source extraction method is developed. Method: We present a deflation-based algorithm utilizing higher order cumulants to analyze the JpJI-MDU source model. The algorithm maximizes a cost function which leads to an eigenvalue problem solved with thin-SVD (singular value decomposition)...
Investigation of thrust effect on the vibrational characteristics of flexible guided missiles
, Article Journal of Sound and Vibration ; Volume 272, Issue 1-2 , 2004 , Pages 287-299 ; 0022460X (ISSN) ; Assadian, N ; Sharif University of Technology
Academic Press
2004
Abstract
In this paper the effect of thrust on the bending behaviour of flexible missiles is investigated. For this purpose, the governing equations of motion of a flexible guided missile are derived following the Lagrangian approach. The missile is idealized as a non-uniform beam where the bending elastic deflections are modelled using the method of modal substitution. The vehicle (time varying) bending modeshapes and natural frequencies are determined by modelling variable mass and stiffness distributions with thrust and mass burning effects accounted for. To solve this problem the missile is divided into several segments of uniform stiffness, density and axial force distribution. This approach...
Investigation of the transient growth in plane jet by non-modal stability analysis
, Article Fluid Dynamics Research ; Volume 51, Issue 5 , 2019 ; 01695983 (ISSN) ; Afshin, H ; Farhanieh, B ; Sharif University of Technology
Institute of Physics Publishing
2019
Abstract
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...