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Series Method (series + method)

Distribution by Scientific Domains
Engineering66%

Selected Abstracts

Analyzing dynamic performance of stressed power systems in vicinity of instability by modal series method

EUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 8 2009
Ali 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]

Analytical power series solutions to the two-dimensional advection,dispersion equation with distance-dependent dispersivities

HYDROLOGICAL PROCESSES, Issue 24 2008
Jui-Sheng Chen
Abstract As is frequently cited, dispersivity increases with solute travel distance in the subsurface. This behaviour has been attributed to the inherent spatial variation of the pore water velocity in geological porous media. Analytically solving the advection,dispersion equation with distance-dependent dispersivity is extremely difficult because the governing equation coefficients are dependent upon the distance variable. This study presents an analytical technique to solve a two-dimensional (2D) advection,dispersion equation with linear distance-dependent longitudinal and transverse dispersivities for describing solute transport in a uniform flow field. The analytical approach is developed by applying the extended power series method coupled with the Laplace and finite Fourier cosine transforms. The developed solution is then compared to the corresponding numerical solution to assess its accuracy and robustness. The results demonstrate that the breakthrough curves at different spatial locations obtained from the power series solution show good agreement with those obtained from the numerical solution. However, owing to the limited numerical operation for large values of the power series functions, the developed analytical solution can only be numerically evaluated when the values of longitudinal dispersivity/distance ratio eL exceed 0·075. Moreover, breakthrough curves obtained from the distance-dependent solution are compared with those from the constant dispersivity solution to investigate the relationship between the transport parameters. Our numerical experiments demonstrate that a previously derived relationship is invalid for large eL values. The analytical power series solution derived in this study is efficient and can be a useful tool for future studies in the field of 2D and distance-dependent dispersive transport. Copyright © 2008 John Wiley & Sons, Ltd. [source]

A new numerical algorithm for sub-optimal control of earthquake excited linear structures

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2001
Mehmet Bakioglu
Abstract Exact optimal classical closed,open-loop control is not achievable for the buildings under seismic excitations since it requires the whole knowledge of earthquake in the control interval. In this study, a new numerical algorithm for the sub-optimal solution of the optimal closed,open-loop control is proposed based on the prediction of near-future earthquake excitation using the Taylor series method and the Kalman filtering technique. It is shown numerically that how the solution is related to the predicted earthquake acceleration values. Simulation results show that the proposed numerical algorithm are better than the closed-loop control and the instantaneous optimal control and proposed numerical solution will approach the exact optimal solution if the more distant future values of the earthquake excitation can be predicted more precisely. Effectiveness of the Kalman filtering technique is also confirmed by comparing the predicted and the observed time history of NS component of the 1940 El Centro earthquake. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Highly accurate solutions for the confined hydrogen atom

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 7 2007
N. Aquino
Abstract The model of the confined hydrogen atom (CHA) was developed by Michels et al. 1 in the mid-1930s to study matter subject to extreme pressure. However, since the eigenvalues cannot be obtained analytically, even the most accurate calculations have yielded little more than 10 figure accuracy. In this work, we show that it is possible to obtain the CHA eigenvalues with extremely high accuracy (up to 100 decimal digits) and we do that using two completely different methods. The first is based on formal solution of the confluent hypergeometric function while the second uses a series method. We also compare radial expectation values obtained by both methods and conclude that the wave functions obtained by these two different approaches are of high quality. In addition, we compute the hyperfine splitting constant, magnetic screening constant, polarizability in the Kirkwood approximation, and pressure as a function of the box radius. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source]

The Price-Volatility Feedback Rate: An Implementable Mathematical Indicator of Market Stability

MATHEMATICAL FINANCE, Issue 1 2003
Emilio Barucci
Geometric analysis of iterated cross-volatilities of asset prices is adopted to assess the stability of the (risk-free) measure under infinitesimal perturbations. Perturbations of asset prices evolve through time according to an ordinary linear differential equation (hedged transfer). The decay (feedback) rate is explicitly computed through a Fourier series method implemented on high frequency time series. [source]