Search for: eigenvalues-and-eigenfunctions
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#### Some lower bounds for the energy of graphs

, Article Linear Algebra and Its Applications ; Volume 591 , 2020 , Pages 205-214 Akbari, S ; Ghodrati, A. H ; Hosseinzadeh, M. A ; Sharif University of Technology
Elsevier Inc  2020
Abstract
The singular values of a matrix A are defined as the square roots of the eigenvalues of A⁎A, and the energy of A denoted by E(A) is the sum of its singular values. The energy of a graph G, E(G), is defined as the sum of absolute values of the eigenvalues of its adjacency matrix. In this paper, we prove that if A is a Hermitian matrix with the block form A=(BDD⁎C), then E(A)≥2E(D). Also, we show that if G is a graph and H is a spanning subgraph of G such that E(H) is an edge cut of G, then E(H)≤E(G), i.e., adding any number of edges to each part of a bipartite graph does not decrease its energy. Let G be a connected graph of order n and size m with the adjacency matrix A. It is well-known...

#### 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

#### Bending-torsional stability analysis of aerodynamically covered pipes with inclined terminal nozzle and concurrent internal and external flows

, Article Journal of Fluids and Structures ; Volume 94 , 2020 Askarian, A. R ; Rahmanian, M ; Haddadpour, H ; Dehghani Firouz Abadi, R ; Sharif University of Technology
Abstract
Stability analysis of a cantilevered pipe with an inclined terminal nozzle as well as simultaneous internal and external fluid flows is investigated in this study. The pipe is embedded in an aerodynamic cover with negligible mass and stiffness simply to streamline the external flow and avoid vortex induced vibrations. The structure of pipe is modeled as an Euler–Bernoulli beam and effects of internal fluid flow including flow-induced inertia, Coriolis and centrifugal forces and the follower force induced by the exhausting jet are taken into account. In addition, neglecting the compressibility effect and using the unsteady Wagner model, aerodynamic loading is determined as a distributed...

#### Free vibration of joined cylindrical–hemispherical FGM shells

, Article Archive of Applied Mechanics ; Volume 90, Issue 10 , 2020 , Pages 2185-2199 Bagheri, H ; Kiani, Y ; Bagheri, N ; Eslami, M. R ; Sharif University of Technology
Springer  2020
Abstract
Free vibration response of a joined shell system including cylindrical and spherical shells is analyzed in this research. It is assumed that the system of joined shell is made from a functionally graded material (FGM). Properties of the shells are assumed to be graded through the thickness. Both shells are unified in thickness. To capture the effects of through-the-thickness shear deformations and rotary inertias, first-order shear deformation theory of shells is used. The Donnell type of kinematic assumptions is adopted to establish the general equations of motion and the associated boundary and continuity conditions with the aid of Hamilton’s principle. The resulting system of equations is...

#### 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 Elyasi, M ; 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...

#### 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...

#### Eigenvectors of deformed Wigner random matrices

, Article IEEE Transactions on Information Theory ; 18 November , 2020 Haddadi, F ; Amini, A ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc  2020
Abstract
We investigate eigenvectors of rank-one deformations of random matrices B = A + θuu* in which A ∈ RN×N is a Wigner real symmetric random matrix, θ ∈ R+, and u is uniformly distributed on the unit sphere. It is well known that for θ > 1 the eigenvector associated with the largest eigenvalue of B closely estimates u asymptotically, while for θ < 1 the eigenvectors of B are uninformative about u. We examine O(1/N) correlation of eigenvectors with u before phase transition and show that eigenvectors with larger eigenvalue exhibit stronger alignment with deforming vector through an explicit inverse law 1/θ*-x with θ* := θ + 1/θ. This distribution function will be shown to be the ordinary...

#### Vibrations and stability analysis of double current-carrying strips interacting with magnetic field

, Article Acta Mechanica ; 2020 Hosseinian, A. R ; Firouz Abadi, R. D ; Sharif University of Technology
Springer  2020
Abstract
Interactive vibrations and buckling of double current-carrying strips (DCCS) are investigated in this study. Considering the rotational and transverse deformation of the strip, four coupled equations of motion are obtained using Hamilton’s principle. Using the Galerkin method, mass and stiffness matrices are extracted and the stability of the system is determined by solving the eigenvalue problem. Effects of pretension and elevated temperature on the stability of DCCS are studied for three types of materials and various arrangements. Finally, the effect of horizontal or vertical distance between strips on the critical current value is investigated. According to the results, the effects of...

#### A screw dislocation near a damaged arbitrary inhomogeneity–matrix interface

, Article International Journal of Damage Mechanics ; Volume 29, Issue 2 , 2020 , Pages 272-296 Kamali, M. T ; Shodja, H. M ; Masoudvaziri, N ; Sharif University of Technology
SAGE Publications Ltd  2020
Abstract
In the literature, the analytical solutions concerned with the interaction between screw dislocation and surfaces/interfaces have been mainly limited to simple geometries and perfect interfaces. The focus of the current work is to provide an approach based on a rigorous semi-analytical theory suitable for treatment of such surfaces/interfaces that concurrently have complex geometry and imperfect bonding. The proposed approach captures the singularity of the elastic fields exactly. A vast variety of the pertinent interaction problems such as dislocation near a multi-inhomogeneity with arbitrary geometry bonded imperfectly to a matrix, dislocation near the free boundaries of a finite elastic...

#### 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...

#### Hybrid anisotropic pentamode mechanical metamaterial produced by additive manufacturing technique

, Article Applied Physics Letters ; Volume 117, Issue 6 , 2020 Mohammadi, K ; Movahhedy, M. R ; Shishkovsky, I ; Hedayati, R ; Sharif University of Technology
American Institute of Physics Inc  2020
Abstract
Pentamode metamaterials are a type of extremal designer metamaterials, which are able to demonstrate extremely high rigidity in one direction and extremely high compliance in other directions. Pentamodes can, therefore, be considered as building blocks of exotic materials with any arbitrarily selected thermodynamically admissible elasticity tensor. The pentamode lattices can then be envisioned to be combined to construct intermediate extremal materials, such as quadramodes, trimodes, and bimodes. In this study, we constructed several primary types of anisotropic pentamode lattices (with midpoint positioning of 10%, 15%, 20%, 25%, 30%, 35%, and 42% of the main unit cell diagonal) and then...

#### 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 Pakravan, M ; 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)...

#### Stabilization of nonlinear dynamic systems over limited capacity communication channels

, Article IEEE Transactions on Automatic Control ; Volume 65, Issue 8 , 2020 , Pages 3655-3662 Sanjaroon, V ; Farhadi, A ; Seyed Motahari, A ; Hosain Khalaj, B ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc  2020
Abstract
This article addresses the stabilization of noiseless nonlinear dynamic systems over limited capacity communication channels. It is shown that the stability of nonlinear dynamic systems over memory-less communication channels implies an inequality condition between the Shannon channel capacity and the summation of the positive equilibrium Lyapunov exponents of the dynamic system or, equivalently, the logarithms of the magnitude of the unstable eigenvalues of system Jacobian. Furthermore, we propose an encoder, decoder, and a controller to prove that scalar nonlinear dynamic systems are stabilizable under the aforementioned inequality condition over the digital noiseless and the packet...

#### An analytic methodology to determine generators redispatch for proactive damping of critical electromechanical oscillations

, Article International Journal of Electrical Power and Energy Systems ; Volume 123 , 2020 Setareh, M ; Parniani, M ; Aminifar, F ; Sharif University of Technology
Elsevier Ltd  2020
Abstract
This paper presents a model-based method for applying online proactive generators redispatch to improve damping of the critical electromechanical oscillations of power system. The proposed method comprises two stages: 1) monitoring modal characteristics of oscillatory modes in ambient condition, and 2) applying generators redispatch based on sensitivities of the critical mode to the generators active power changes using a new analytic method. An online identification method such as error feedback lattice recursive least square adaptive filter is applied for online estimation of the oscillatory modes. Then, whenever the damping ratio of an identified mode is less than a preset threshold, its...

#### Efficient, Fair, and QoS-Aware policies for wirelessly powered communication networks

, Article IEEE Transactions on Communications ; Volume 68, Issue 9 , 2020 , Pages 5892-5907 Rezaei, R ; Omidvar, N ; Movahednasab, M ; Pakravan, M. R ; Sun, S ; Guan, Y. L ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc  2020
Abstract
In this paper, we propose efficient wireless power transfer (WPT) policies for various practical scenarios in wirelessly powered communication networks (WPCNs). First, we consider WPT from an energy access point (E-AP) to multiple energy receivers (E-Rs). We formulate the problem of maximizing the total average received power of the E-Rs subject to power constraints of the E-AP, which is a non-convex stochastic optimization problem. Using eigenvalue decomposition techniques, we derive a closed-form expression for the optimal policy, which requires the distribution of the channel state information (CSI) in the network. We then propose a near-optimal policy that does not require this knowledge...

#### 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 largest eigenvalue of signed unicyclic graphs

, Article Linear Algebra and Its Applications ; Volume 581 , 2019 , Pages 145-162 ; 00243795 (ISSN) Akbari, S ; Belardo, F ; Heydari, F ; Maghasedi, M ; Souri, M ; Sharif University of Technology
Elsevier Inc  2019
Abstract
Signed graphs are graphs whose edges get signs ±1 and, as for unsigned graphs, they can be studied by means of graph matrices. Here we focus our attention to the largest eigenvalue, also known as the index of the adjacency matrix of signed graphs. Firstly we give some general results on the index variation when the corresponding signed graph is perturbed. Also, we determine signed graphs achieving the minimal or the maximal index in the class of unbalanced unicyclic graphs of order n≥3. © 2019

#### 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...

#### 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
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...