Sharif Digital Repository

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  

In this paper, we argue that in many basic algorithms for machine learning, including support vector machine (SVM) for classification, principal component analysis (PCA) for dimensionality reduction, and regression for dependency estimation, we need the inner products of the data samples, rather than the data samples themselves.Motivated by the above observation, we introduce the problem of private inner product retrieval for distributed machine learning, where we have a system including a database of some files, duplicated across some non-colluding servers. A user intends to retrieve a subset of specific size of the set of the inner product of every pair of data items in the database with... 

Tape mechanisms must be able to transport the tape with a constant velocity for achieving high rate of data transfer. In this paper, a multivariable model of tape transport mechanism including the take-up and supply reel servos for tape tension control and capstan servo for speed control is considered. To achieve desired performance,pole-placement approach based on general canonical control form (GCCF) is used. Instead of using expensive tension sensors, an observer is designed. A regulator system is developed for disturbance rejection; and a modified integral control is designed for perfect tracking of desired setpoints in tape speed and tensions. Since the real dynamic model associates... 

To achieve high rate of data transfer, tape mechanisms must be able to transport the tape with a constant velocity for scanning. During this process, it is desired to make the rise time minimized without timing and data transfer errors. In this paper, three servo systems including the take-up and supply reel servos for tape tension control and capstan servo for speed control are considered. So, tape transport mechanisms can be described with a nonlinear multi-input multi-output system (MIMO). After state-space representation of the problem, feedback control is designed for tracking objective. It should be mentioned that an increase in the speed of time response of system corresponds to an... 

Tape mechanisms must be able to transport the tape with a constant velocity for achieving high rate of data transfer. In this paper, a multivariable model of tape transport mechanism including the take-up and supply reel servos for tape tension control and capstan servo for speed control is considered. To achieve desired performance,pole-placement approach based on general canonical control form (GCCF) is used. Instead of using expensive tension sensors, an observer is designed. A regulator system is developed for disturbance rejection; and a modified integral control is designed for perfect tracking of desired setpoints in tape speed and tensions. Since the real dynamic model associates... 

In this paper, a robotic manipulator modelled as a cantilever rotating Euler-Bernoulli beam is considered. Control objective is achieving a desired angular rotation of the manipulator tip while its lateral vibration is suppressed. An external driving torque is the control input of the system. Two dynamic transfer functions are derived to describe beam tip motion and angular rotation in terms of the desired angular rotation. After state-space representation of the problem, an observer is designed to estimate state variables of the system. Then, a feedback control is designed for both regulation and tracking objectives. Eigenvalues are chosen such that an appropriate response is achieved while... 

To achieve high rate of data transfer, tape mechanisms must be able to transport the tape with a constant velocity for scanning. During this process, it is desired to make the rise time minimized without timing and data transfer errors. In this paper, three servo systems including the take-up and supply reel servos for tape tension control and capstan servo for speed control are considered. So, tape transport mechanisms can be described with a nonlinear multi-input multi-output system (MIMO). After state-space representation of the problem, feedback control is designed for tracking objective. It should be mentioned that an increase in the speed of time response of system corresponds to an... 

During the year, due to weather conditions, the temperature fluctuations at surface level cause problems in underground pipes as a result of freezing water. One of the best prevention strategies is the use of polyurethane floor insulation for keeping the temperature of clay above zero degrees Celsius. In this study to calculate the minimum thickness of polyurethane insulation layer, the differential equation of energy is solved based on principle of separation of variables using imaginary eigenvalues for consistency with the temperature distribution in multi-layer consist of asphalt, gravel and polyurethane with finite thickness and clay as a semiinfinite medium with periodic thermal... 

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... 

We consider the problem of distributing two conducting materials in a ball with xed proportion in order to minimize the rst eigenvalue of a Dirichlet operator. It was conjectured that the optimal distribution consists of putting the material with the highest conductivity in a ball around the center. In this paper, we show that the conjecture is false for all dimensions greater than or equal to two  

Singular spectrum analysis (SSA) is a well-studied approach in signal processing. SSA has originally been designed to extract information from short noisy chaotic time series and to enhance the signal-to-noise ratio. SSA is good for offline applications; however, many applications, such as modelling, analysis, and prediction of time-varying and non-stationary time series, demand for online analysis. This study introduces a recursive algorithm called recursive SSA as a modification to regular SSA for dynamic and online applications. The proposed method is based on eigenvector matrix perturbation approach. After recursively calculating the covariance matrix of the trajectory matrix, R-SSA... 

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... 

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... 

In this paper, the development of a neutron noise simulator for hexagonal-structured reactor cores using both the forward and the adjoint methods is reported. The spatial discretisation of both 2-D 2-group static and dynamic equations is based on a developed box-scheme finite difference method for hexagonal mesh boxes. Using the power iteration method for the static calculations, the 2-group neutron flux and its adjoint with the corresponding eigenvalues are obtained by the developed static simulator. The results are then benchmarked against the well-known CITATION computer code. The dynamic calculations are performed in the frequency domain which leads to discarding of the time... 

The nonlinear free and forced bending vibration of sandwich plates with incompressible viscoelastic core is investigated under the effects of different source of nonlinearities. For the core constrained between stiffer layers, the transverse shear strains, as well as the rotations are assumed to be moderate. The linear and quadratic displacement fields are also adopted for the in-plane and out-of-plane displacements of the core, respectively. The assumption of moderate transverse strains requires a nonlinear constitutive equation which is obtained from a single-integral nonlinear viscoelastic model using the assumed order of magnitudes for linear strains and rotations. The 5th-order method... 

This paper proposes a new distributed cooperative secondary control for both frequency and voltage restoration of an islanded microgrid with droop-controlled, inverter-based distributed generations (DGs). Existing distributed methods commonly design secondary control based on the minimum real part of the nonzero Laplacian matrix eigenvalues related to the microgrid communication graph, which, however, is global information. In contrast to the existing distributed methods, in this paper we design a fully distributed adaptive control based on the dynamic model of DG units and on information from neighboring units. Therefore, the proposed control scheme increases the system reliability,... 

The present article intends to provide a size-dependent generalized thermoelasticity model and closed-form solution for thermoelastic damping (TED) in cylindrical nanoshells. With the aim of incorporating size effect within constitutive relations and heat conduction equation, nonlocal elasticity theory and Guyer–Krumhansl (GK) heat conduction model are exploited. Donnell–Mushtari–Vlasov (DMV) equations are also employed to model the cylindrical nanoshell. By adopting asymmetric simple harmonic form for oscillations of nanoshell and merging the motion, compatibility and heat conduction equations, the nonclassical frequency equation is extracted. By solving this eigenvalue problem and... 

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... 

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... 

The Differential Transfer Matrix Method is extended to the complex plane, which allows dealing with singularities at turning points. The results for real-valued systems are simplified and a pair of basis functions are found. These bases are a bit less accurate than WKB solutions but much easier to work with because of their algebraic form. Furthermore, these bases exactly satisfy the initial conditions and may go over the turning points without the divergent behavior of WKB solutions. The findings of this paper allow explicit evaluation of eigenvalues of confined modes with high precision, as demonstrated by few examples