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

, Article Acta Mechanica ; Volume 232, Issue 1 , 2021 , Pages 229-245 ; 00015970 (ISSN) ; Firouz Abadi, R. D ; Sharif University of Technology
Springer
2021

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...

#### Stability analysis for design improvement of bio-inspired flapping wings by energy method

, Article Aerospace Science and Technology ; Volume 111 , 2021 ; 12709638 (ISSN) ; Banazadeh, A ; Sharif University of Technology
Elsevier Masson s.r.l
2021

Abstract

This study attempts to reach a broad understanding of the stability properties of nonlinear time-periodic flapping wing structures. Two bio-system models, Hummingbird (6DOF) and Hawkmoth (3DOF) are developed for this purpose. Initial analysis on the Hummingbird model, which is based on the Floquet theory, kinetic energy integration, and phase portrait technique, indicates lack of stability in hover flight. Kinetic energy integration is carried out on the extended model of the Hawkmoth to find the domain of attraction and increase the level of stability by varying the design parameters. Here, the hinge location of the wing, flapping amplitude, flapping frequency, and mean angle of attack are...

#### Non-fragile h∞ order reduction of LTI controllers

, Article IEEE Control Systems Letters ; Volume 5, Issue 1 , 2021 , Pages 163-168 ; 24751456 (ISSN) ; Nobakhti, A ; Tavazoei, M. S ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2021

Abstract

The eigenvalue perturbation theorem is used to propose a convex fragility criterion with application to control system design. The criterion can be considered as a non-normality measure of the controller state-space matrix. Non-normality of a matrix is defined as its distance to the nearest real normal matrix within a convex normal subspace. Based on the criterion, an H∞ method for the order reduction of linear time-invariant (LTI) controllers is developed which leads to non-fragile reduced order controllers. 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission

#### Effect of axially graded constraining layer on the free vibration properties of three layered sandwich beams with magnetorheological fluid core

, Article Composite Structures ; Volume 255 , 2021 ; 02638223 (ISSN) ; Asgari, M ; Haddadpour, H ; Sharif University of Technology
Elsevier Ltd
2021

Abstract

The free linear vibration of an adaptive sandwich beam consisting of a frequency and field-dependent magnetorheological fluid core and an axially functionally graded constraining layer is investigated. The Euler-Bernoulli and Timoshenko beam theories are utilized for defining the longitudinal and lateral deformation of the sandwich beam. The Rayleigh-Ritz method is used to derive the frequency-dependent eigenvalue problem through the kinetic and strain energy expressions of the sandwich beam. In order to deal with the frequency dependency of the core, the approached complex eigenmodes method is implemented. The validity of the formulation and solution method is confirmed through comparison...

#### Tele-operation of autonomous vehicles over additive white Gaussian noise channel

, Article Scientia Iranica ; Volume 28, Issue 3 , 2021 , Pages 1592-1605 ; 10263098 (ISSN) ; Farhadi, A ; Sharif University of Technology
Sharif University of Technology
2021

Abstract

This paper is concerned with the tele-operation of autonomous vehicles over analog Additive White Gaussian Noise (AWGN) channel, which is subject to transmission noise and power constraint. The nonlinear dynamic of autonomous vehicles is described by the unicycle model and is cascaded with a bandpass filter acting as encoder. Using the describing function method, the nonlinear dynamic of autonomous vehicles is represented by an approximate linear system. Then, the available results for linear control over analog AWGN channel are extended to account for linear continuous time systems with non-real valued and multiple real valued eigenvalues and for tracking a non-zero reference signal....

#### A note on the algebraic connectivity of a graph and its complement

, Article Linear and Multilinear Algebra ; Volume 69, Issue 7 , 2021 , Pages 1248-1254 ; 03081087 (ISSN) ; Akbari, S ; Sharif University of Technology
Taylor and Francis Ltd
2021

Abstract

For a graph G, let (Formula presented.) denote its second smallest Laplacian eigenvalue. It was conjectured that (Formula presented.), where (Formula presented.) is the complement of G. In this paper, it is shown that (Formula presented.). © 2019 Informa UK Limited, trading as Taylor & Francis Group

#### Gold at crossroads of radical generation and scavenging at density functional theory level: Nitrogen and oxygen free radicals versus their precursors in the face of nanogold

, Article Journal of Physical Organic Chemistry ; Volume 34, Issue 1 , 2021 ; 08943230 (ISSN) ; Kassaee, M. Z ; Ayoubi Chianeh, M ; Fattahi, A ; Sharif University of Technology
John Wiley and Sons Ltd
2021

Abstract

In our previous report (J. Phys. Org. Chem., 2017), we discussed the dual behavior of gold nanocluster (Au3 NC), where it scavenged reactive oxygen species (ROS) while promoted their generation to a lesser extent. Continuing this quest, we investigate the effects of Au3 NC on common reactive nitrogen species (RNS: O=N˙ and O=N-O) and their precursors (O=N-H and O=N-O-H, respectively), at B3LYP/LACVP+* level of theory. We compare the results with those of prevalent ROS (H-O˙ and H-O-O˙) and their precursors (H-O-H and H-O-O-H, respectively). To this end, various parameters are probed such as binding energy (Eb), bond dissociation energy (BDE), bond lengths, Mullikan spin density (MSD),...

#### Hypoenergetic and nonhypoenergetic digraphs

, Article Linear Algebra and Its Applications ; Volume 618 , 2021 , Pages 129-143 ; 00243795 (ISSN) ; Das, K. C ; Khalashi Ghezelahmad, S ; Koorepazan Moftakhar, F ; Sharif University of Technology
Elsevier Inc
2021

Abstract

The energy of a graph G, E(G), is the sum of absolute values of the eigenvalues of its adjacency matrix. This concept was extended by Nikiforov to arbitrary complex matrices. Recall that the trace norm of a digraph D is defined as, N(D)=∑i=1nσi, where σ1≥⋯≥σn are the singular values of the adjacency matrix of D. In this paper we would like to present some lower and upper bounds for N(D). For any digraph D it is proved that N(D)≥rank(D) and the equality holds if and only if D is a disjoint union of directed cycles and directed paths. Finally, we present a lower bound on σ1 and N(D) in terms of the size of digraph D. © 2021 Elsevier Inc

#### The main eigenvalues of signed graphs

, Article Linear Algebra and Its Applications ; Volume 614 , 2021 , Pages 270-280 ; 00243795 (ISSN) ; França, F. A. M ; Ghasemian, E ; Javarsineh, M ; de Lima, L. S ; Sharif University of Technology
Elsevier Inc
2021

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

#### A note on the algebraic connectivity of a graph and its complement

, Article Linear and Multilinear Algebra ; Volume 69, Issue 7 , 2021 , Pages 1248-1254 ; 03081087 (ISSN) ; Akbari, S ; Sharif University of Technology
Taylor and Francis Ltd
2021

Abstract

For a graph G, let (Formula presented.) denote its second smallest Laplacian eigenvalue. It was conjectured that (Formula presented.), where (Formula presented.) is the complement of G. In this paper, it is shown that (Formula presented.). © 2019 Informa UK Limited, trading as Taylor & Francis Group

#### Gold at crossroads of radical generation and scavenging at density functional theory level: Nitrogen and oxygen free radicals versus their precursors in the face of nanogold

, Article Journal of Physical Organic Chemistry ; Volume 34, Issue 1 , 2021 ; 08943230 (ISSN) ; Kassaee, M.Z ; Ayoubi-Chianeh, M ; Fattahi, A ; Sharif University of Technology
John Wiley and Sons Ltd
2021

Abstract

In our previous report (J. Phys. Org. Chem., 2017), we discussed the dual behavior of gold nanocluster (Au3 NC), where it scavenged reactive oxygen species (ROS) while promoted their generation to a lesser extent. Continuing this quest, we investigate the effects of Au3 NC on common reactive nitrogen species (RNS: O=N˙ and O=N-O) and their precursors (O=N-H and O=N-O-H, respectively), at B3LYP/LACVP+* level of theory. We compare the results with those of prevalent ROS (H-O˙ and H-O-O˙) and their precursors (H-O-H and H-O-O-H, respectively). To this end, various parameters are probed such as binding energy (Eb), bond dissociation energy (BDE), bond lengths, Mullikan spin density (MSD),...

#### Spectra of strongly Deza graphs

, Article Discrete Mathematics ; Volume 344, Issue 12 , 2021 ; 0012365X (ISSN) ; Haemers, W. H ; Hosseinzadeh, M. A ; Kabanov, V. V ; Konstantinova, E. V ; Shalaginov, L ; Sharif University of Technology
Elsevier B.V
2021

Abstract

A Deza graph G with parameters (n,k,b,a) is a k-regular graph with n vertices such that any two distinct vertices have b or a common neighbours. The children GA and GB of a Deza graph G are defined on the vertex set of G such that every two distinct vertices are adjacent in GA or GB if and only if they have a or b common neighbours, respectively. A strongly Deza graph is a Deza graph with strongly regular children. In this paper we give a spectral characterisation of strongly Deza graphs, show relationships between eigenvalues, and study strongly Deza graphs which are distance-regular. © 2021 Elsevier B.V

#### Hypoenergetic and nonhypoenergetic digraphs

, Article Linear Algebra and Its Applications ; Volume 618 , 2021 , Pages 129-143 ; 00243795 (ISSN) ; Das, K. C ; Khalashi Ghezelahmad, S ; Koorepazan Moftakhar, F ; Sharif University of Technology
Elsevier Inc
2021

Abstract

The energy of a graph G, E(G), is the sum of absolute values of the eigenvalues of its adjacency matrix. This concept was extended by Nikiforov to arbitrary complex matrices. Recall that the trace norm of a digraph D is defined as, N(D)=∑i=1nσi, where σ1≥⋯≥σn are the singular values of the adjacency matrix of D. In this paper we would like to present some lower and upper bounds for N(D). For any digraph D it is proved that N(D)≥rank(D) and the equality holds if and only if D is a disjoint union of directed cycles and directed paths. Finally, we present a lower bound on σ1 and N(D) in terms of the size of digraph D. © 2021 Elsevier Inc

#### The main eigenvalues of signed graphs

, Article Linear Algebra and Its Applications ; Volume 614 , 2021 , Pages 270-280 ; 00243795 (ISSN) ; França, F. A. M ; Ghasemian, E ; Javarsineh, M ; de Lima, L. S ; Sharif University of Technology
Elsevier Inc
2021

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

#### Eigenvectors of deformed wigner random matrices

, Article IEEE Transactions on Information Theory ; Volume 67, Issue 2 , 2021 , Pages 1069-1079 ; 00189448 (ISSN) ; Amini, A ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2021

Abstract

We investigate eigenvectors of rank-one deformations of random matrices boldsymbol B = boldsymbol A + theta boldsymbol {uu}{} in which boldsymbol A in mathbb R{N times N} is a Wigner real symmetric random matrix, theta in mathbb R{+} , and boldsymbol u is uniformly distributed on the unit sphere. It is well known that for theta > 1 the eigenvector associated with the largest eigenvalue of boldsymbol B closely estimates boldsymbol u asymptotically, while for theta < 1 the eigenvectors of boldsymbol B are uninformative about boldsymbol u. We examine mathcal O({1}/{N}) correlation of eigenvectors with boldsymbol u before phase transition and show that eigenvectors with larger eigenvalue exhibit...

#### 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...

#### Some lower bounds for the energy of graphs

, Article Linear Algebra and Its Applications ; Volume 591 , 2020 , Pages 205-214 ; 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 ; 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

#### On edge-path eigenvalues of graphs

, Article Linear and Multilinear Algebra ; 2020 ; Azizi, S ; Ghorbani, M ; Li, X ; Sharif University of Technology
Taylor and Francis Ltd
2020

Abstract

Let G be a graph with vertex set (Formula presented.) and (Formula presented.) be an (Formula presented.) matrix whose (Formula presented.) -entry is the maximum number of internally edge-disjoint paths between (Formula presented.) and (Formula presented.), if (Formula presented.), and zero otherwise. Also, define (Formula presented.), where D is a diagonal matrix whose i-th diagonal element is the number of edge-disjoint cycles containing (Formula presented.), whose (Formula presented.) is a multiple of J−I. Among other results, we determine the spectrum and the energy of the matrix (Formula presented.) for an arbitrary bicyclic graph G. © 2020 Informa UK Limited, trading as Taylor &...

#### The main eigenvalues of signed graphs

, Article Linear Algebra and Its Applications ; 2020 ; 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