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A comparative study of two preconditioners for solving 3D inviscid low speed flows
, Article Applied Mechanics and Materials ; Volume 110-116 , 2012 , Pages 423-430 ; 16609336 (ISSN) ; 9783037852620 (ISBN) ; Moghadam, R. K ; Sharif University of Technology
2012
Abstract
In the present study, two preconditioners proposed by Eriksson, and Choi and Merkel are implemented on a 3D upwind Euler flow solver on unstructured meshes. The mathematical formulations of these preconditioning schemes for the set of primitive variables Q→p 1=[ρ u v , w p] T are drawn and their eigenvalues and eigenvectors are compared with each others. A cell-centered finite volume Roe's method is used for discretization of the 3D preconditioned Euler equations. The accuracy and performance of these preconditioning schemes are examined by computing low Mach number flows over the ONERA M6 wing for different conditions
Graetz problem extended to mixed electroosmotically and pressure-driven flow
, Article Journal of Thermophysics and Heat Transfer ; Volume 26, Issue 1 , 2012 , Pages 123-133 ; 08878722 (ISSN) ; Veisi, H ; Saidi, M. H ; Chakraborty, S ; Sharif University of Technology
2012
Abstract
Thermally developing mixed electroosmotically and pressure-driven flow in a parallel plate microchannel with a step change in wall temperature is considered in the framework of an extended Graetz problem. Both Joule heating and viscous dissipation effects are taken into consideration. Expressions for the dimensionless temperature and Nusselt number in the form of infinite series are presented. In general, the associated eigenvalue problem is solved numerically. Nevertheless, an analytical solution is also presented for axial locations close to the entrance. Comparisons are made between the present results and those obtained by approximating the electroosmotic velocity with the...
Parametric study of the dynamic response of thin rectangular plates traversed by a moving mass
, Article Acta Mechanica ; Volume 223, Issue 1 , September , 2012 , Pages 15-27 ; 00015970 (ISSN) ; Rofooei, F. R ; Sharif University of Technology
2012
Abstract
The governing differential equation of motion of a thin rectangular plate excited by a moving mass is considered. The moving mass is traversing on the plate's surface at arbitrary trajectories. Eigenfunction expansion method is employed to solve the constitutive equation of motion for various boundary conditions. Approximate and exact expressions of the inertial effects are adopted for the problem formulation. In the approximate formulation, only the vertical acceleration component of the moving mass is considered while in the exact formulation all the convective acceleration components are included in the problem formulation as well. Parametric studies are carried out to investigate the...
Conformal upper bounds for the eigenvalues of the Laplacian and Steklov problem
, Article Journal of Functional Analysis ; Volume 261, Issue 12 , 2011 , Pages 3419-3436 ; 00221236 (ISSN) ; Sharif University of Technology
2011
Abstract
In this paper, we find upper bounds for the eigenvalues of the Laplacian in the conformal class of a compact Riemannian manifold (M,g). These upper bounds depend only on the dimension and a conformal invariant that we call "min-conformal volume". Asymptotically, these bounds are consistent with the Weyl law and improve previous results by Korevaar and Yang and Yau. The proof relies on the construction of a suitable family of disjoint domains providing supports for a family of test functions. This method is interesting for itself and powerful. As a further application of the method we obtain an upper bound for the eigenvalues of the Steklov problem in a domain with C1 boundary in a complete...
Free vibration analysis of FGM beams with different boundary conditions using RKPM meshless method
, Article Proceedings of the ASME Design Engineering Technical Conference, 28 August 2011 through 31 August 2011 ; Volume 1, Issue PARTS A AND B , August , 2011 , Pages 1187-1191 ; 9780791854785 (ISBN) ; Ahmadian, M. T ; Sharif University of Technology
Abstract
This paper presents free vibration analysis of functionally graded material (FGM) beams with different boundary conditions, using RKPM (Reproducing Kernel Particle Method), which is a meshless method. System of equations of motion is derived by using Lagrange's method under the assumption of Euler-Bernoulli beam theory. Boundary conditions of beam are taken into account by using Lagrange multipliers. It is assumed that material properties of the beam vary continuously in the thickness direction according to the power-law form. RKPM is applied to obtain eigenvalue equation of vibration and natural frequencies are obtained. It should be noted that for special cases where the beam is uniform,...
Transmit beampattern synthesis using eigenvalue decomposition in MIMO radar
, Article ICICS 2011 - 8th International Conference on Information, Communications and Signal Processing, 13 December 2011 through 16 December 2011 ; December , 2011 , Page(s): 1 - 5 ; 9781457700309 (ISBN) ; Behnia, F ; Sharif University of Technology
2011
Abstract
MIMO radar is the next generation radar which transmits arbitrary waveforms at each one of its apertures. It has been shown that design of waveforms for MIMO radars in order to synthesize a desired spatial beampattern is mapped into a waveform correlation matrix (R) design in the narrowband case. Searching for desired R has been modeled as a convex optimization problem which demands considerable processing power. There are also some close form solutions for special cases like rectangular beampatterns. Here we deal with the problem from a matrix eigenvalue theory perspective and show how close form solutions can be found for more general cases relaxing high computational power demand. Our...
An innovative implementation of Circular Hough Transform using eigenvalues of Covariance Matrix for detecting circles
, Article Proceedings Elmar - International Symposium Electronics in Marine, 14 September 2011 through 16 September 2011, Zadar ; 2011 , Pages 397-400 ; 13342630 (ISSN) ; 9789537044121 (ISBN) ; Mianroodi, J. R ; Norouzi, N ; Khajooeizadeh, A ; Sharif University of Technology
2011
Abstract
In this paper, a fast and accurate algorithm for identifying circular objects in images is proposed. The presented method is a robust, fast and optimized adaption of Circular Hough Transform (CHT), Eigenvalues of Covariance Matrix and K-means clustering techniques. Results are greatly improved by implementing iterative K-means clustering algorithm and establishing an exponential growth instead of updating values in the parameter space of CHT through summation, both in runtime and quality. In fact, using the Eigenvalues of Covariance Matrix as a validating method, a well balanced compromise between the speed and accuracy of results is achieved. This method is tested on several real world...
Recursive spectral analysis of natural time series based on eigenvector matrix perturbation for online applications
, Article IET Signal Processing ; Volume 5, Issue 6 , 2011 , Pages 515-526 ; 17519675 (ISSN) ; Lucas, C ; Araabi, B. N ; Moshiri, B ; Bidar, M. R ; Sharif University of Technology
2011
Abstract
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...
Hippocampal shape analysis in epilepsy using Laplace-Beltrami spectrum
, Article 2011 19th Iranian Conference on Electrical Engineering, ICEE 2011, 17 May 2011 through 19 May 2011 ; May , 2011 , Page(s): 1 - 5 ; ISSN : 21647054 ; 9789644634284 (ISBN) ; Soltanian Zadeh, H ; Moghadasi, S. R ; Sharif University of Technology
2011
Abstract
Shape analysis plays an important role in many medical imaging studies. One of the recent shape analysis methods uses the Laplace Beltrami eigenvalues which is also used in this paper for global shape comparison of hippocampus of normal subjects and epileptic patients. Popularity of the Laplace Beltrami operator in this field is due to its isometry-invariance which avoids pre-processing steps like mapping, registration, and alignment. In addition, it is capable of revealing fine details in shapes that makes this method a good choice for deformation detecting purposes like epilepsy diagnosis. To examine capability of the proposed method, statistical analysis and two ways of classification,...
On edge star sets in trees
, Article Discrete Mathematics ; Volume 311, Issue 13 , July , 2011 , Pages 1172-1178 ; 0012365X (ISSN) ; Ghorbani, E ; Mahmoodi, A ; Sharif University of Technology
2011
Abstract
Let A be a Hermitian matrix whose graph is G (i.e. there is an edge between the vertices i and j in G if and only if the (i,j) entry of A is non-zero). Let λ be an eigenvalue of A with multiplicity mA(λ). An edge e=ij is said to be Parter (resp., neutral, downer) for λ,A if mA(λ)-mA-e(λ) is negative (resp., 0, positive ), where A-e is the matrix resulting from making the (i,j) and (j,i) entries of A zero. For a tree T with adjacency matrix A a subset S of the edge set of G is called an edge star set for an eigenvalue λ of A, if |S|=mA(λ) and A-S has no eigenvalue λ. In this paper the existence of downer edges and edge star sets for non-zero eigenvalues of the adjacency matrix of a tree is...
A lower bound for algebraic connectivity based on the connection-graph- stability method
, Article Linear Algebra and Its Applications ; Volume 435, Issue 1 , Sep , 2011 , Pages 186-192 ; 00243795 (ISSN) ; Jalili, M ; Hasler, M ; Sharif University of Technology
2011
Abstract
This paper introduces the connection-graph-stability method and uses it to establish a new lower bound on the algebraic connectivity of graphs (the second smallest eigenvalue of the Laplacian matrix of the graph) that is sharper than the previously published bounds. The connection-graph-stability score for each edge is defined as the sum of the lengths of the shortest paths making use of that edge. We prove that the algebraic connectivity of the graph is bounded below by the size of the graph divided by the maximum connection-graph-stability score assigned to the edges
Computing all the Floquet eigenfunctions of oscillators using harmonic balance Jacobian matrices
, Article IET Circuits, Devices and Systems ; Volume 5, Issue 4 , July , 2011 , Pages 257-266 ; 1751858X (ISSN) ; Farzaneh, F ; Sharif University of Technology
2011
Abstract
Floquet eigenfunctions and Floquet exponents are encountered in stability and noise analysis of circuits operating at large signal periodic regime. It is analytically verified that the spectrum vectors of the left-hand and right-hand Floquet eigenfunctions and the Floquet exponents (Floquet eigenpairs) are members of the harmonic balance eigenvalues and eigenvectors (HB eigenpairs). The relationships between other HB eigenpairs with the Floquet eigenpairs are discussed. This discussion leads to a practical algorithm for computing the Floquet eigenpairs through HB eigenpairs. Furthermore, it is analytically verified that the main arguments of the study are consistent with the...
On the existence of an analytic solution to the 1-D Ising model with nearest and next-nearest neighbor interactions in the presence of a magnetic field
, Article Phase Transitions ; Volume 84, Issue 1 , Dec , 2011 , Pages 77-84 ; 01411594 (ISSN) ; Daryaei, E ; Abroshan, H ; Akbarzadeh, H ; Parsafar, G ; Fortunelli, A ; Sharif University of Technology
2011
Abstract
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...
Direct synthesis of fixed-order h∞ controllers
, Article IEEE Transactions on Automatic Control ; Volume 60, Issue 10 , July , 2015 , Pages 2704-2709 ; 00189286 (ISSN) ; Nobakhti, A ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2015
Abstract
This technical note considers the fixed-order H∞ output feedback control design problem for linear time invariant (LTI)systems. The objective is to design a fixed-order controller with guaranteed stability and closed-loop H∞ performance. This problem is NP-hard due to the non-convex rank constraint which appears in the formulation. We propose an algorithm for non-iterative direct synthesis (NODS) of reduced order robust controllers. NODS entails initial computation of two positive-definite matrices via full-order convex LMI conditions. These are then utilized by appropriate eigenvalue decomposition to directly obtain a suboptimal convex formulation for the fixed-order controller
Galerkin and Generalized Least Squares finite element: A comparative study for multi-group diffusion solvers
, Article Progress in Nuclear Energy ; Volume 85 , 2015 , Pages 473-490 ; 01491970 (ISSN) ; Saadatian Derakhshandeh, F ; Sharif University of Technology
Elsevier Ltd
2015
Abstract
Abstract In this paper, the solution of multi-group neutron/adjoint equation using Finite Element Method (FEM) for hexagonal and rectangular reactor cores is reported. The spatial discretization of the neutron diffusion equation is performed based on two different Finite Element Methods (FEMs) using unstructured triangular elements generated by Gambit software. Calculations are performed using Galerkin and Generalized Least Squares FEMs; based on which results are compared. Using the power iteration method for the neutron and adjoint calculations, the neutron and adjoint flux distributions with the corresponding eigenvalues are obtained. The results are then validated against the valid...
An exact method for the extraction of effective bulk and surface parameters of periodic artificial media
, Article IEEE Transactions on Antennas and Propagation ; Volume 63, Issue 6 , 2015 , Pages 2521-2531 ; 0018926X (ISSN) ; Rejaei, B ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2015
Abstract
A new method is presented for the extraction of the bulk and surface parameters of a periodic artificial medium which uses the eigenvectors of the generalized transfer matrix of a unit layer. These eigenvectors correspond to the Bloch modes of the periodic structure. The eigenvector related to the propagating Bloch mode directly yields an expression for the effective, intrinsic wave impedance of the medium. Moreover, the interface between the artificial material and a surrounding, conventional (dielectric) region is described by an interface impedance matrix which accounts for the excitation of higher order, nonpropagating Bloch modes at the interface. Although these modes do not propagate...
Denoising of ictal EEG data using semi-blind source separation methods based on time-frequency priors
, Article IEEE Journal of Biomedical and Health Informatics ; Volume 19, Issue 3 , July , 2015 , Pages 839-847 ; 21682194 (ISSN) ; Shamsollahi, M. B ; Albera, L ; Merlet, I ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2015
Abstract
Removing muscle activity from ictal ElectroEncephaloGram (EEG) data is an essential preprocessing step in diagnosis and study of epileptic disorders. Indeed, at the very beginning of seizures, ictal EEG has a low amplitude and its morphology in the time domain is quite similar to muscular activity. Contrary to the time domain, ictal signals have specific characteristics in the time-frequency domain. In this paper, we use the time-frequency signature of ictal discharges as a priori information on the sources of interest. To extract the time-frequency signature of ictal sources, we use the Canonical Correlation Analysis (CCA) method. Then, we propose two time-frequency based semi-blind source...
Optimal pinning controllability of complex networks: Dependence on network structure
, Article Physical Review E - Statistical, Nonlinear, and Soft Matter Physics ; Volume 91, Issue 1 , January , 2015 ; 15393755 (ISSN) ; Askari Sichani, O ; Yu, X ; Sharif University of Technology
American Physical Society
2015
Abstract
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...
Dynamic response of a non-uniform Timoshenko beam, subjected to moving mass
, Article Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science ; Volume 229, Issue 14 , October , 2015 , Pages 2499-2513 ; 09544062 (ISSN) ; Mofid, M ; Ghannadiasl, A ; Sharif University of Technology
SAGE Publications Ltd
2015
Abstract
In this article, the dynamic response of a non-uniform Timoshenko beam acted upon by a moving mass is extensively investigated. To this end, the eigenfunction expansion method is adapted to the problem, employing the natural mode shapes of a uniform Timoshenko beam. Moreover, the orthonormal polynomial series expansion method is successfully applied to the coupled set of governing differential equations pertaining to the dynamic behavior of non-uniform Timoshenko beam actuated by a moving mass. Some numerical examples are solved in which the excellent agreement of the two presented methods is illustrated
Modal analysis of the dynamic response of Timoshenko beam under moving mass
, Article Scientia Iranica ; Volume 22, Issue 2 , 2015 , Pages 331-344 ; 10263098 (ISSN) ; Mofid, M ; Ghannadiasl, A ; Sharif University of Technology
Sharif University of Technology
2015
Abstract
In this study, the dynamic response of a Timoshenko beam under moving mass is investigated. To this end, vectorial form orthogonality property of the Timoshenko beam free vibration modes is applied to the EEM (Eigenfunction Expansion Method). The implication of the vectorial form series and an appropriate inner product of mode shapes in combination are focused for a beam with arbitrary boundary conditions. Consequently, significant simplifications and efficacy in the utilization of the EEM in eliminating the spatial domain is achieved. In order to comprise validation, the present study is compared with the DET (Discrete Element Technique) and the RKPM (Reproducing Kernel Particle Method)