Sharif Digital Repository

A generalized Hubbard model based on a molecular approach is used to calculate many electron wavefunctions of diamond vacancies. We have calculated the oscillator strength of the dipole transition rates from the ground states of the neutral and negatively charged vacancies. The ratio of the oscillator strengths is in very good quantitative agreement with the reported optical spectroscopic data. Electronic configurations in the ground and dipole allowed excited states are presented. With the proposed picture, the much larger oscillator strength of the negatively charged vacancy with respect to other experimentally investigated color centers N-V, H3, X3 and H4 is explained  

Controlling networked structures has many applications in science and engineering. In this paper, we consider the problem of pinning control (pinning the dynamics into the reference state), and optimally placing the driver nodes, i.e., the nodes to which the control signal is fed. Considering the local controllability concept, a metric based on the eigenvalues of the Laplacian matrix is taken into account as a measure of controllability. We show that the proposed optimal placement strategy considerably outperforms heuristic methods including choosing hub nodes with high degree or betweenness centrality as drivers. We also study properties of optimal drivers in terms of various centrality... 

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... 

In the present study, considering two-dimensional porosity distribution through a functionally graded porous (FGP) beam, its optimal distributions are obtained. A multi-objective optimization problem is defined to maximize critical buckling load and minimize mass of the beam, simultaneously. To this end, Timoshenko beam theory is employed and equilibrium equations for two-dimensional functionally graded porous (2D-FGP) beam are derived. For the solution, we present generalized differential quadrature method (GDQM) and consider two symmetric boundary conditions (Clamped-Clamped and Hinged-Hinged). Solving generalized eigenvalue problem, critical buckling load for 2D-FGP beam is then obtained.... 

Waveform design for Target identification and classification in MIMO radar systems has been studied in several recent works. While the previous works considered signal independent noise, here we extend the results to the case where signal-dependent noise, clutter, is also present and then we find the optimum waveform for several estimators differing in the assumptions on the given statistics. Computing the optimal waveforms for MMSE estimator leads to the Semi-definite programming (SDP) problem. Finding the optimal transmit signals for CSLS estimator results in a minimax eigenvalue problem. Finally it is shown that equal power waveforms are the best transmit signals for the SLS estimator.... 

It is has been long known that the curved space in the presence of gravitation can be described as a non-homogeneous anisotropic medium in flat geometry with different constitutive equations. In this article, we show that the eigenpolarizations of such medium can be exactly solved, leading to a pseudo-isotropic description of curved vacuum with two refractive index eigenvalues having opposite signs, which correspond to forward and backward travel in time. We conclude that for a rotating universe, time-reversal symmetry is broken. We also demonstrate the applicability of this method to Schwarzschild metric and derive exact forms of refractive index. We derive the subtle optical anisotropy of... 

In this paper, numerical investigation of the statical and dynamical stability of aligned and misaligned viscoelastic cantilevered beam is performed with a terminal nozzle in the presence of gravity in two cases: (1) effect of fluid velocity on the flutter boundary of beam conveying fluid and (2) effect of gravity on the buckling boundary of beam conveying fluid. The beam is assumed to have a large width-to-thickness ratio, so the out-of-plane bending rigidity is far higher than the in-plane bending and torsional rigidities. Gravity vector is considered in the vertical direction. Thus, deflection of the beam because of the gravity effect couples the in-plane bending and torsional equations.... 

A system is called prescribed-time attractive if its solution converges at an arbitrary user-defined finite time. In this note, necessary and sufficient conditions are developed for the prescribed-time attractivity of linear time-varying (LTV) systems. It is proved that the frozen-time eigenvalues of a prescribed-time attractive LTV system have negative real parts when the time is sufficiently close to the convergence moment. This result shows that the ubiquitous singularity problem of prescribed-time attractive LTV systems can be avoided without instability effects by switching to the corresponding frozen-time system at an appropriate time. Consequently, it is proved that the time-varying... 

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... 

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  

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... 

To solve the controversy, regarding the existence of an analytic solution to the 1-D Ising model with nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions in the presence of a magnetic field, we apply the transfer matrix method to solve the 1-D Ising model in the presence of a magnetic field, taking both NN and NNN interactions into account. We show that it is possible to write a transfer matrix only if the number of sites is even. Even in such a case, it is impossible to diagonalize the transfer matrix in an analytic form. Therefore, we employ a numerical method to obtain the eigenvalues of the transfer matrix. Moreover, the heat capacity, magnetization, and magnetic... 

The energy of a graph G, E(G), is defined as the sum of absolute values of the eigenvalues of its adjacency matrix. In Akbari and Hosseinzadeh (2020) [3] it was conjectured that for every graph G with maximum degree Δ(G) and minimum degree δ(G) whose adjacency matrix is non-singular, E(G)≥Δ(G)+δ(G) and the equality holds if and only if G is a complete graph. Let G be a connected graph with the edge set E(G). In this paper, first we show that E(L(G))≥|E(G)|+Δ(G)−5, where L(G) denotes the line graph of G. Next, using this result, we prove the validity of the conjecture for the line of each connected graph of order at least 7. © 2021 Elsevier Inc  

Let L be a reversible Markovian generator on a finite set V. Relations between the spectral decomposition of L and subpartitions of the state space V into a given number of components which are optimal with respect to min-max or max-min Dirichlet connectivity criteria are investigated. Links are made with higher-order Cheeger inequalities and with a generic characterization of subpartitions given by the nodal domains of an eigenfunction. These considerations are applied to generators whose positive rates are supported by the edges of a discrete cycle Z N, to obtain a full description of their spectra and of the shapes of their eigenfunctions, as well as an interpretation of the spectrum... 

This paper studies mixed-mode shear band propagation behaviors in porous plastic dilatant materials by the extended finite element method (XFEM). The Drucker-Prager elastoplastic model is combined with the strong discontinuity method to simulate the dilatant shear band. First, the dissipative nature of the localized area with displacement jump is integrated into the constitutive model by introducing a cohesive law. A new contribution lies that the yielding function is modified in the localized region to calculate the cohesive traction within the framework of the XFEM. The shear band propagation direction is determined by the singularity of the acoustic tensor and the corresponding... 

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... 

This paper presents a method for nonlinear aeroelastic analysis of Human Powered Aircraft (HPA) wings. In this type of aircraft there is a long, highly flexible wing. Wing flexibility, coupled with long wing span can lead to large deflections during normal flight operation; therefore, a wing in vertical and torsional motion using the second-order form of nonlinear general flexible Euler-Bernoulli beam equations is used for structural modeling. Unsteady linear aerodynamic theory based on Wagner function is used for determination of aerodynamic loading on the wing. Combining these two types of formulations yields the nonlinear integro-differentials aeroelastic equations. Using the Galerkin's... 

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  

Denoising is an important preprocessing stage in some Electroencephalography (EEG) applications such as epileptic source localization. In this paper, we propose a new algorithm for denoising the interictal EEG data. The proposed algorithm is based on Generalized Eigenvalue Decomposition of two covariance matrices of the observations. Since one of these matrices is related to the spike durations, we should estimate the occurrence time of the spike peaks and the exact spike durations. To this end, we propose a spike detection algorithm which is based on the available spike detection methods. The comparison of the results of the proposed algorithm with the results of two well-known ICA... 

Least squares estimation is a widely-used technique for range-based source localization, which obtains the most probable position of mobile station. These methods cannot provide desirable accuracy in the case with a non line of sight (NLOS) path between mobile station and base stations. To circumvent this drawback, many algorithms have been proposed to identify and mitigate this error; however, they have a large run-time overhead. On the other hand, new positioning systems utilize a large set of base stations, and a practical algorithm should be fast enough to deal with them. In this paper, we propose a novel algorithm based on subspace method to identify and eliminate the NLOS error....