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    Computing all the Floquet eigenfunctions of oscillators using harmonic balance Jacobian matrices

    , Article IET Circuits, Devices and Systems ; Volume 5, Issue 4 , July , 2011 , Pages 257-266 ; 1751858X (ISSN) Jahanbakht, S ; Farzaneh, F ; Sharif University of Technology
    2011
    Abstract
    Floquet eigenfunctions and Floquet exponents are encountered in stability and noise analysis of circuits operating at large signal periodic regime. It is analytically verified that the spectrum vectors of the left-hand and right-hand Floquet eigenfunctions and the Floquet exponents (Floquet eigenpairs) are members of the harmonic balance eigenvalues and eigenvectors (HB eigenpairs). The relationships between other HB eigenpairs with the Floquet eigenpairs are discussed. This discussion leads to a practical algorithm for computing the Floquet eigenpairs through HB eigenpairs. Furthermore, it is analytically verified that the main arguments of the study are consistent with the... 

    A heterogeneous diffusive logistic model of a single species population dynamics with predation and harvesting terms

    , Article Nonlinear Analysis, Theory, Methods and Applications ; Volume 156 , 2017 , Pages 1-16 ; 0362546X (ISSN) Shabani Rokn E Vafa, S ; Torabi Tehrani, H ; Sharif University of Technology
    Abstract
    We study existence and multiplicity of positive solutions of a heterogeneous diffusive logistic equation with predation and harvesting terms, −Δu=au−b(x)u2−c, where a,c,m and d are positive constants, Ω a bounded smooth domain in RN, and b(x) is a nonnegative function on Ω¯, with Ω0 a region such that Ω¯0⊂Ω and Ω¯0={x∈Ω:b(x)=0}. Under the strong growth rate assumption, that is, when a is greater than the first eigenvalue of −Δ in Ω0 with Dirichlet boundary condition, we show that the equation has at least one positive solution for 0≤d0. In addition, in case c

    Rewirings based on the eigenvectors of the laplacian matrix for enhancing synchronizability of dynamical networks

    , Article 2009 7th IEEE International Conference on Industrial Informatics, INDIN 2009, Cardiff, 23 June 2009 through 26 June 2009 ; 2009 , Pages 588-593 ; 19354576 (ISSN); 9781424437603 (ISBN) Jalili, M ; Ajdari Rad, A ; Sharif University of Technology
    2009
    Abstract
    Synchronizability of dynamical networks can be defined as the ease by which the network synchronizes its activity. We propose a method for enhancing the synchronizability of dynamical networks by efficient rewirings. The method is based on the eigenvectors corresponding to the second smallest and the largest eigenvalue of the Laplacian matrix and a modified version of the simulated annealing approach is used to perform the optimization task. Starting from a simple network, i.e. an undirected and unweighted network, and at each step, an edge is selected for disconnection and two non-adjacent nodes for creating at edge in between. The effectiveness of the algorithm is tested on artificially... 

    Application of the modified reduced-order aerodynamics modelling approach to aeroelastic analysis

    , Article Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering ; Volume 223, Issue 3 , 2009 , Pages 257-270 ; 09544100 (ISSN) Shahverdi, H ; Salehzadeh Nobari, A ; Haddadpour, H ; Behbahani Nejad, M ; Sharif University of Technology
    2009
    Abstract
    This study presents the application of the Proposed Modified Reduced-Order Aerodynamics Modelling approach for aeroelastic analysis based on the boundary element method (BEM) as a novel approach. The used BEM has the capability to capture the thickness effect and geometric complexity of a general three-dimensional model. In this approach the reduced-order aerodynamic model is defined through the eigenvalue problem of unsteady flow based on the unknown wake singularities. Based on the used aerodynamic model an explicit algebraic form of the aeroelastic equations is derived that reduces computational efforts and complexity. This special feature enables us to determine the aeroelastic... 

    Strong structural controllability of signed networks

    , Article 58th IEEE Conference on Decision and Control, CDC 2019, 11 December 2019 through 13 December 2019 ; Volume 2019-December , 2019 , Pages 4557-4562 ; 07431546 (ISSN); 9781728113982 (ISBN) Mousavi, S. S ; Haeri, M ; Mesbahi, M ; Sharif University of Technology
    Institute of Electrical and Electronics Engineers Inc  2019
    Abstract
    In this paper, we discuss the controllability of a family of linear time-invariant (LTI) networks defined on a signed graph. In this direction, we introduce the notion of positive and negative signed zero forcing sets for the controllability analysis of positive and negative eigenvalues of system matrices with the same sign pattern. A sufficient combinatorial condition that ensures the strong structural controllability of signed networks is then proposed. Moreover, an upper bound on the maximum multiplicity of positive and negative eigenvalues associated with a signed graph is provided. © 2019 IEEE  

    On the minimum energy of regular graphs

    , Article Linear Algebra and Its Applications ; Volume 581 , 2019 , Pages 51-71 ; 00243795 (ISSN) Aashtab, A ; Akbari, S ; Ghasemian, E ; Ghodrati, A. H ; Hosseinzadeh, M. A ; Koorepazan Moftakhar, F ; Sharif University of Technology
    Elsevier Inc  2019
    Abstract
    The energy of a graph G, E(G), is the sum of absolute values of the eigenvalues of its adjacency matrix. Gutman et al. proved that for every cubic graph of order n, E(G)≥n. Here, we improve this result by showing that if G is a connected subcubic graph of order n≥8, then E(G)≥1.01n. Also, we prove that if G is a traceable subcubic graph of order n≥8, then E(G)>1.1n. Let G be a connected cubic graph of order n≥8, it is shown that E(G)>n+2. It was proved that if G is a connected cubic graph of order n, then E(G)≤1.65n. Also, in this paper we would like to present the best lower bound for the energy of a connected cubic graph. We introduce an infinite family of connected cubic graphs whose for... 

    Fast estimation of propagation constants in lamellar gratings needless of solving the eigenvalue equation

    , Article 27th Iranian Conference on Electrical Engineering, ICEE 2019, 30 April 2019 through 2 May 2019 ; 2019 , Pages 1342-1346 ; 9781728115085 (ISBN) Faghihifar, E ; Akbari, M ; Hossein Nekuee, S. A ; Sharif University of Technology
    Institute of Electrical and Electronics Engineers Inc  2019
    Abstract
    Fourier-based modal methods are among the most significant tools for accurate numerical analysis of grating structures. However, they mostly lead to time consuming and memory hungry eigenvalue problems, particularly when large dielectric constants or high contrasts are involved. We have found an asymptotic semi-empirical relationship for the propagation constants of a lamellar grating, obtained from Fourier-based modal methods. Hence, given any truncation order, it is possible to estimate propagation constants without having to solve the eigenvalue equation. We observed propagation constants only depend on permittivities, filling factors, and the unit cell size, while the dependence on the... 

    Extraction of effective constitutive parameters of artificial media using Bloch modes

    , Article Journal of the Optical Society of America B: Optical Physics ; Volume 36, Issue 11 , 2019 , Pages 3226-3235 ; 07403224 (ISSN) Sheikh Ansari, A ; Rejaei, B ; Sharif University of Technology
    OSA - The Optical Society  2019
    Abstract
    The effective constitutive parameters of a three-dimensional periodic structure are calculated using its Bloch modes. These modes and their propagation constants are obtained from eigenvectors and eigenvalues of the generalized transfer matrix of a unit layer of the structure. Effective bulk permittivity and permeability tensors of the medium are obtained when two of the Bloch modes are dominant, i.e., propagate without significant decay inside the medium. The effect of the strongly decaying Bloch modes, which are excited at the interface with a conventional medium, are included by means of surface impedance matrices. The results are in excellent agreement with full-wave electromagnetic... 

    Extraction of effective constitutive parameters of artificial media using bloch modes

    , Article Journal of the Optical Society of America B: Optical Physics ; Volume 36, Issue 11 , 2019 , Pages 3226-3235 ; 07403224 (ISSN) Sheikh Ansari, A ; Rejaei, B ; Sharif University of Technology
    OSA - The Optical Society  2019
    Abstract
    The effective constitutive parameters of a three-dimensional periodic structure are calculated using its Bloch modes. These modes and their propagation constants are obtained from eigenvectors and eigenvalues of the generalized transfer matrix of a unit layer of the structure. Effective bulk permittivity and permeability tensors of the medium are obtained when two of the Bloch modes are dominant, i.e., propagate without significant decay inside the medium. The effect of the strongly decaying Bloch modes, which are excited at the interface with a conventional medium, are included by means of surface impedance matrices. The results are in excellent agreement with full-wave electromagnetic... 

    Trees with a large Laplacian eigenvalue multiplicity

    , Article Linear Algebra and Its Applications ; Volume 586 , 2020 , Pages 262-273 Akbari, S ; van Dam, E. R ; Fakharan, M. H ; Sharif University of Technology
    Elsevier Inc  2020
    Abstract
    In this paper, we study the multiplicity of the Laplacian eigenvalues of trees. It is known that for trees, integer Laplacian eigenvalues larger than 1 are simple and also the multiplicity of Laplacian eigenvalue 1 has been well studied before. Here we consider the multiplicities of the other (non-integral) Laplacian eigenvalues. We give an upper bound and determine the trees of order n that have a multiplicity that is close to the upper bound [Formula presented], and emphasize the particular role of the algebraic connectivity. © 2019 Elsevier Inc  

    The main eigenvalues of signed graphs

    , Article Linear Algebra and Its Applications ; 2020 Akbari, S ; França, F. A. M ; Ghasemian, E ; Javarsineh, M ; de Lima, L. S ; Sharif University of Technology
    Elsevier Inc  2020
    Abstract
    A signed graph Gσ is an ordered pair (V(G),E(G)), where V(G) and E(G) are the set of vertices and edges of G, respectively, along with a map σ that signs every edge of G with +1 or −1. An eigenvalue of the associated adjacency matrix of Gσ, denoted by A(Gσ), is a main eigenvalue if the corresponding eigenspace has a non-orthogonal eigenvector to the all-one vector j. We conjectured that for every graph G≠K2,K4{e}, there is a switching σ such that all eigenvalues of Gσ are main. We show that this conjecture holds for every Cayley graphs, distance-regular graphs, vertex and edge-transitive graphs as well as double stars and paths. © 2020 Elsevier Inc  

    Fast estimation of propagation constants in crossed gratings

    , Article Journal of Optics (United Kingdom) ; Volume 22, Issue 2 , 2020 Faghihifar, E ; Akbari, M ; Nekuee, S. A. H ; Sharif University of Technology
    IOP Publishing Ltd  2020
    Abstract
    Fourier-based modal methods are among the most effective numerical tools for the accurate analysis of crossed gratings. However, leading to computationally expensive eigenvalue equations significantly restricts their applicability, particularly when large truncation orders are required. The resultant eigenvalues are the longitudinal propagation constants of the grating and play a key role in applying the boundary conditions, as well as in the convergence and stability analyses. This paper aims to propose simple techniques for the fast estimation of propagation constants in crossed gratings, predominantly with no need to solve an eigenvalue equation. In particular, we show that for regular... 

    Optimal exploitation of the resource in remote state preparation

    , Article Physical Review A ; Volume 102, Issue 1 , 15 July , 2020 Nikaeen, M ; Ramezani, M ; Bahrampour, A ; Sharif University of Technology
    American Physical Society  2020
    Abstract
    Transmission efficiency (TE) of remote state preparation (RSP) with a shared quantum state and one bit of classical communication is considered. Following Dakić et al. [Nat. Phys. 8, 666 (2012)10.1038/nphys2377], the encoding and decoding operators of the protocol are restricted to the physically relevant classes of projective measurements and unitary operators, respectively. It is shown that contrary to the previous arguments, the quadratic fidelity as well as the linear fidelity could be a valid figure of merit to quantify the TE of RSP. Then, the TE of the protocol in terms of both linear and quadratic fidelities is evaluated in a fully optimized scenario which includes the maximization... 

    Analytical extraction of leaky modes in circular slab waveguides with arbitrary refractive index profile

    , Article Applied Optics ; Volume 46, Issue 36 , 2007 , Pages 8656-8667 ; 1559128X (ISSN) Sarrafi, P ; Zareian, N ; Mehrany, K ; Sharif University of Technology
    2007
    Abstract
    Circular slab waveguides are conformally transformed into straight inhomogeneous waveguides, where-upon electromagnetic fields in the core are expanded in terms of Legendre polynomial basis functions. Thereafter, different analytical expression of electromagnetic fields in the cladding region, viz. Wentzel-Kramers-Brillouin solution, modified Airy function expansion, and the exact field solution for circular waveguides, i.e., Hankel function of complex order, are each matched to the polynomial expansion of the transverse electric field within the guide. This field matching process renders different boundary conditions to be satisfied by the set of orthogonal Legendre polynomial basis... 

    Hermite polynomial expansion for analysis of electromagnetic slow waves in coupled nano conducting layer with Gaussian profile

    , Article LAPC 2007: 3rd Loughborough Antennas and Propagation Conference, Loughborough, 2 April 2007 through 3 April 2007 ; 2007 , Pages 265-268 ; 1424407761 (ISBN); 9781424407767 (ISBN) Sarrafi, P ; Mehrany, K ; Rashidian, B ; Sharif University of Technology
    2007
    Abstract
    The possibility of electromagnetic slow wave propagation in dielectric slab waveguides, when free two-dimensional interface charge layers are generated at film-substrate and film-cover interfaces, is already explored. In this paper, the propagation of electromagnetic slow waves supported by induced charge layers of nonzero thickness, whose induced charge densities have Gaussian profiles, is investigated for the first time. In order to analyze the effects of inhomogeneity in the conductivity profile, the electric field is expanded in terms of Hermite polynomials and each eigenmode is sought in the complete space spanned by them. © 2007 IEEE  

    Passivity enforcement via residues perturbation for admittance representation of power system components

    , Article Iranian Journal of Science and Technology, Transaction B: Engineering ; Volume 31, Issue 3 , 2007 , Pages 273-288 ; 03601307 (ISSN) Porkar, B ; Vakilian, M ; Shahrtash, M ; Iravani, M. R ; Sharif University of Technology
    2007
    Abstract
    Employing an admittance representation in the form of a black box model approximated by rational functions for linear power system components or network equivalents to be included in electromagnetic transient studies is a well-known method which improves calculation efficiency. All of the methods that have been proposed to solve the rational approximation problem have made efforts to overcome the problem of preserving the passivity of the final model. Passivity is a vital property, since a non-passive model may lead to an unstable transient simulation in the time domain. In this paper a post-processing technique for passivity enforcement through an iterative process for the detection and... 

    Buckling of cracked cylindrical thin shells under combined internal pressure and axial compression

    , Article Thin-Walled Structures ; Volume 44, Issue 2 , 2006 , Pages 141-151 ; 02638231 (ISSN) Vaziri, A ; Estekanchi, H. E ; Sharif University of Technology
    2006
    Abstract
    Linear eigenvalue analysis of cracked cylindrical shells under combined internal pressure and axial compression is carried out to study the effect of crack type, size and orientation on the buckling behavior of cylindrical thin shells. Two types of crack are considered; through crack and thumbnail crack. Our calculations indicate that depending on the crack type, length, orientation and the internal pressure, local buckling may precede the global buckling of the cylindrical shell. The internal pressure, in general, increases the buckling load associated with the global buckling mode of the cylindrical shells. In contrast, the effect of internal pressure on buckling loads associated with the... 

    Simple model for exact heave motion of tension leg platform

    , Article WSEAS Transactions on Mathematics ; Volume 5, Issue 5 , 2006 , Pages 500-506 ; 11092769 (ISSN) Tabeshpour, M. R ; Golafshani, A. A ; Seif, M. S ; Sharif University of Technology
    2006
    Abstract
    In this paper the dynamic response of the leg of a tension leg platform (tether) subjected to the load simulated as ocean wave at the top of the leg is presented. The structural model is very simple but several complicated factors such as foundation effect, buoyancy and simulated ocean wave load are considered. Two continuous models are proposed to present the structural system and the mentioned effects. The problem is solved by means of non-harmonic Fourier expansion in terms of eigenfunctions obtained from a non-regular Sturm-Liouville system  

    Hippocampal shape analysis in the Laplace Beltrami feature space for temporal lobe epilepsy diagnosis and lateralization

    , Article Proceedings - International Symposium on Biomedical Imaging ; 2012 , Pages 150-153 ; 19457928 (ISSN) ; 9781457718588 (ISBN) Shishegar, R ; Gandomkar, Z ; Soltaman Zadeh, H ; Moghadasi, S. R ; Sharif University of Technology
    IEEE  2012
    Abstract
    Shape analysis plays an important role in many medical imaging studies. One of the recent shape analysis methods uses the Laplace Beltrami operator which is also used in this paper for hippocampal shape comparison. We proposed a feature vector which consists of size measures and shape descriptors based on Laplace Beltrami eigenvalues and eigenfunctions. The aforementioned feature space is utilised for automatic differentiating normal subjects from epileptic patients as well as distinguishing epileptic patients with left temporal lobe epilepsy (LTLE) from patients with right temporal lobe epilepsy (RTLE). Achieved results are diagnostic accuracy of 93% with 95% sensitivity and lateralization... 

    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 Khavasi, E ; 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...