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Similarity Transformations (similarity + transformation)
Selected AbstractsAnalyzing dynamic performance of stressed power systems in vicinity of instability by modal series methodEUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 8 2009Ali H. Naghshbandy Abstract Highly stressed power systems exhibit complex dynamic behaviors such as inter-area oscillations when subjected to large disturbances. In such conditions, nonlinear effects have dominant role in determining dynamic response of the systems. In this paper by using modal series method, dynamic behaviors of the stressed power systems in severe conditions and near instability have been studied. Also two measures, mode dominance measure (MDM) and most perturbed machine factor (MPF) have been introduced. They determine the most dominant modes and identify the most perturbed generators when the system is subjected to a given fault. Contribution factors have been used to show the links between identified modes and machines from the analysis. Time domain simulation has been helped for validation of the results. By using similarity transformation, state variables have been represented in modal space and utilized to check the results. The studies are carried out on the IEEE 50-generator test system which demonstrates a wide range of dynamic characteristics at different loading levels and fault scenarios. Copyright © 2008 John Wiley & Sons, Ltd. [source] Thermal-diffusion and diffusion-thermo effects on convective heat and mass transfer in a visco-elastic fluid flow through a porous medium over a stretching sheetINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2006A. M. Salem Abstract An analysis has been carried out to obtain the thermal-diffusion and diffusion-thermo effects on the mixed free forced convective and mass transfer in a visco-elastic fluid flow through a porous medium over a stretching sheet. Here, the driving force for the flow is provided by an impermeable sheet stretched with a velocity proportional to the distance from a slit and buoyancy effects due to both temperature and concentration gradient. The partial differential equations governing the problem under consideration have been transformed by a similarity transformation into a system of ordinary differential equations which are solved numerically by applying the shooting method. The effects of Soret number, Dufour number, visco-elastic parameter, Porosity parameter, Grashof number and modified Grashof number on the velocity, temperature and concentration have been discussed. Numerical results for the problem considered are given and illustrated graphically. Copyright © 2006 John Wiley & Sons, Ltd. [source] Orthogonal similarity transformation into block-semiseparable matrices of semiseparability rank kNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 10 2005M. Van Barel Abstract Very recently, an algorithm, which reduces any symmetric matrix into a semiseparable one of semi- separability rank 1 by similar orthogonality transformations, has been proposed by Vandebril, Van Barel and Mastronardi. Partial execution of this algorithm computes a semiseparable matrix whose eigenvalues are the Ritz-values obtained by the Lanczos' process applied to the original matrix. Also a kind of nested subspace iteration is performed at each step. In this paper, we generalize the above results and propose an algorithm to reduce any symmetric matrix into a similar block-semiseparable one of semiseparability rank k, with k , ,, by orthogonal similarity transformations. Also in this case partial execution of the algorithm computes a block-semiseparable matrix whose eigenvalues are the Ritz-values obtained by the block-Lanczos' process with k starting vectors, applied to the original matrix. Subspace iteration is performed at each step as well. Copyright © 2005 John Wiley & Sons, Ltd. [source] An implicit QR algorithm for symmetric semiseparable matricesNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 7 2005Raf Vandebril Abstract The QR algorithm is one of the classical methods to compute the eigendecomposition of a matrix. If it is applied on a dense n × n matrix, this algorithm requires O(n3) operations per iteration step. To reduce this complexity for a symmetric matrix to O(n), the original matrix is first reduced to tridiagonal form using orthogonal similarity transformations. In the report (Report TW360, May 2003) a reduction from a symmetric matrix into a similar semiseparable one is described. In this paper a QR algorithm to compute the eigenvalues of semiseparable matrices is designed where each iteration step requires O(n) operations. Hence, combined with the reduction to semiseparable form, the eigenvalues of symmetric matrices can be computed via intermediate semiseparable matrices, instead of tridiagonal ones. The eigenvectors of the intermediate semiseparable matrix will be computed by applying inverse iteration to this matrix. This will be achieved by using an O(n) system solver, for semiseparable matrices. A combination of the previous steps leads to an algorithm for computing the eigenvalue decompositions of semiseparable matrices. Combined with the reduction of a symmetric matrix towards semiseparable form, this algorithm can also be used to calculate the eigenvalue decomposition of symmetric matrices. The presented algorithm has the same order of complexity as the tridiagonal approach, but has larger lower order terms. Numerical experiments illustrate the complexity and the numerical accuracy of the proposed method. Copyright © 2005 John Wiley & Sons, Ltd. [source] Complex quasiperiodic self-similar tilings: their parameterization, boundaries, complexity, growth and symmetryACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2010A. V. Shutov A class of quasiperiodic tilings of the complex plane is discussed. These tilings are based on ,-expansions corresponding to cubic irrationalities. There are three classes of tilings: Q3, Q4 and Q5. These classes consist of three, four and five pairwise similar prototiles, respectively. A simple algorithm for construction of these tilings is considered. This algorithm uses greedy expansions of natural numbers on some sequence. Weak and strong parameterizations for tilings are obtained. Layerwise growth, the complexity function and the structure of fractal boundaries of tilings are studied. The parameterization of vertices and boundaries of tilings, and also similarity transformations of tilings, are considered. [source] Effect of a Magnetic Field on a Micropolar Fluid Flow in the Vicinity of an Axisymmetric Stagnation Point on a Circular CylinderCHEMICAL ENGINEERING & TECHNOLOGY (CET), Issue 8 2009G. M. Abdel-Rahman Abstract The effect of a magnetic field on a micropolar fluid flow in the vicinity of an axisymmetric stagnation point on a circular cylinder is studied numerically. The governing conservation equations of continuity, momentum and angular momentum are partial differential equations which are transformed into a system of ordinary differential equations by using the usual similarity transformations. The resulting system of coupled non-linear ordinary differential equations is solved numerically by using the shooting method. The numerical results indicate the velocity, angular velocity and pressure distributions for different parameters of the problem including Reynolds number, magnetic parameter and dimensionless material properties, etc. In addition, the effect of the pertinent parameters on the local skin friction coefficient and the couple stress are discussed numerically and illustrated graphically. [source] | |||||||||||||