Sharif Digital Repository

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... 

The concept of energy conjugacy for stress and strain measures states that a stress tensor T is conjugate to a strain measure E if T: Ė provides the rate of change of the internal energy per unit reference volume of the body in an adiabatic process. The applications of the conjugate stress and strain measures are in the development of the basic relations in nonlinear analysis of solids. In this paper using eigenprojection method, unified explicit basis-free relation between two arbitrary stress tensors T(f) and T (g), respectively conjugate to two measures of Hill's strains is determined. The result is valid for arbitrary dimension of the Euclidean inner product space and for all cases of... 

In this paper, we consider the network coding in networks with broadcast channels (called hypernetworks) as the first step for applying network coding to wireless networks. We first prove a Max-Flow Min-Cut theorem for such networks. While we propose an algorithm to achieve this bound, we will introduce new definitions and provide sufficient tools to extend many of the theorems stated for flows in wireline networks to the case of hypernetworks. As an example, we will extend the Max-Flow Min-Cut condition for feasibility of the point-to-point connection in wireline networks to the case of hypernetworks. Then, we will extend the algebraic approach of Koetter and Medard in [3] to the... 

Planar grating diffraction analysis based on Legendre expansion of electromagnetic fields is reported. In contrast to conventional RCWA in which the solution is obtained using state variables representation of the coupled wave amplitudes; here, the solution is expanded in terms of Legendre polynomials. This approach, without facing the problem of numerical instability and inevitable round off errors, yields well-behaved algebraic equations for deriving diffraction efficiencies, and can be employed for analysis of different types of gratings. Thanks to the recursive properties of Legendre polynomials, for longitudinally inhomogeneous gratings, wherein differential equations with non-constant... 

A novel approach for photonic crystals devices analysis, based on perturbation theory is reported. In this method the photonic crystal device is considered as the superposition of a parent lattice and a perturbing one. Then the solution is investigated in terms of the eigensolutions of the parent lattice. This way, one can easily obtain analytic expressions within the first order perturbation, describing the effects of different parameters on the eigensolutions of the structure. The perturbation theory employed in this work is typical of what is conventionally used in quantum mechanics literature. The proposed method is explicit, works fast, and does not involve complicated numerical... 

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  

Ab initio total energy calculations have been performed for superconducting GdBa2Cu3O7 and insulating PrBa 2Cu3O7 using the full-potential linear augmented plane-wave method in the local density approximation (LDA) and generalized gradient approximation (GGA). The comparison of the calculated unit cell volume and lattice parameters with the experimental data indicates the improvement of these parameters in the GGA relative to LDA. LDA and GGA give the equilibrium unit cell volume about 6% smaller and 1.25% larger than the experimental data, respectively for both systems. Thus frozen phonon calculations have been performed to determine the eigenvalues and eigenvectors of the k=0 Ag modes of... 

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... 

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... 

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  

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... 

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.... 

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),... 

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  

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  

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),... 

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  

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  

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... 

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...