Sharif Digital Repository

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... 

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... 

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... 

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  

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... 

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... 

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  

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 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  

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  

An assessment study of two different shunt FACTS devices for compensating disturbances due to voltage variation in power systems is presented in this paper. Namely, Static Compensator (STATCOM) and Static Var Compensator (SVC) are Considered in this study. Eigen Value analysis and nonlinear time domain simulations for starting motor, motor in load varying state and short circuit on motor terminals show that STATCOM DC Voltage regulation has a better performance Compared to that of SVC. The result that will be presented in the paper will prove the superiorly of STATCOM over SVC in increasing motor speeding up and improving system voltage profile particularly at starting. © 2005 IEEE  

Here we are concerned with the problem of the existence of periodic solution for certain second and third-order nonlinear differential equations. Our method here is to consider the problem as an eigenvalue problem and treat it by the topological degree theory. In particular we establish the conditions of the existence of periodic solution first for a simpler system which is homotopic to the original system and then generalize the obtained results for the focal system. The method employed here is applicable also for a system of nonlinear differential equations just with simple modifications. Finally, we present some specific examples numerically to show that the results are valid and... 

When applying the equivalent inclusion method (EIM) to a composite material with non-dilute distribution of reinforcement particles, due to the complex interaction between the particles, the homogenizing eigenstrain field will in general be highly nonlinear. The interaction becomes more complex, when the reinforcements are multi-phase particles, i.e., the core inhomogeneity is surrounded by many layers of coatings. In this paper, a treatment for an accurate determination of the distribution of homogenizing eigenstrain fields corresponding to composites with non-dilute periodic distribution of multi-phase reinforcement particles is given. The proposed method is applicable to problems, where... 

This paper presents a new reduced-order modeling approach based on boundary element method. In this approach the eigenvalue problem of the unsteady flows is defined based on the unknown wake singularities. By constructing this reduced-order model, the body quasi-static eigenmodes are removed from the eigensystem and it is possible to obtain satisfactory results without static correction technique when enough eigenmodes are used. In addition to the conventional method, Eigenanalysis and reduced-order modeling of unsteady flows over a NACA 0012 airfoil and a wing with NACA 0012 section are performed using this new ROM method. Numerical examples are presented that demonstrate the accuracy and... 

The behavior of a Jeffcott rotor with lateral-torsional coupling is investigated in the presence of internal and external damping and eccentricity. The governing equations are derived based on the Lagrange method. Also, the Laplace method and linearization is used to solve the governing equations for free vibrations analysis. For a rotor with unbalance, the instability occurs when the real part of eigenvalues has positive values, and at the same time, it is the intersection point between the lines of natural frequencies. The instability speed increases with increasing the external damping, yet dependent on the internal damping and unbalance. Also, it is demonstrated that the rotor critical... 

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  

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... 

It is known that discrete-time controllers, whose state matrices have no non-integer element, are beneficial in homomorphic based encrypted control systems. Nevertheless, it has been recently shown that possessing state matrices with integer elements usually yields unstable discrete-time controllers. In this note, we investigate the problem from a non-minimality perspective. It is shown that non-minimal realizations, in comparison to minimal ones, can theoretically provide a wider framework to obtain controllers having state matrices with integer elements. However, in the case of dealing with BIBO stable controllers, this framework cannot preserve internal stability. But, benefiting from the...