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The paper presents a new method of solving the Telegraphers' equations, resulting in a transmission-line model based on natural modes of oscillation. By means of eigenvalue analysis, it is shown how each natural mode can be accessed individually using a linear transformation. Initially, the model is formed in the frequency domain so as to take account of frequency-dependent parameters and losses, notably arising from skin-effect in the conducting paths. It is then shown how the frequency-domain prototype can be transferred into the time domain using third-order z-transform approximations of the exact frequency domain representation. An illustrative case confirms that it is possible to effect the transition from the frequency domain to the time domain with minimal loss of accuracy. [ABSTRACT FROM AUTHOR]

This paper presents a study on amplitude death in nonlinear coupled oscillators containing fractional derivatives. Analytical criterion for amplitude death region is obtained by eigenvalue analysis and verified by numerical results. It is found that amplitude death regions can be enlarged to a large extent by fractional derivatives. For this reason, amplitude death can be detected in fractional Stuart–Landau systems with weak coupling strength and low frequency, whereas it never appears in integer-order systems. Interestingly, the widening of amplitude death region induced by fractional derivative is shared by a variety of oscillators with different types of coupling mechanisms. An interpretation for the underlying mechanism of this phenomenon is briefly addressed, based on which we further suggest a coupling organization leading to amplitude death only in fractional oscillators. [ABSTRACT FROM AUTHOR]

This work studies the impact on power system dynamics of wind energy conversion systems based on permanent magnet synchronous generators when they perform ancillary services. The ability of modern variable-speed wind turbines to rapidly modify its active and reactive power is exploited in order to provide additional support to the power grid and enhance the overall stability of the system. A set of control loops are incorporated to the wind farm in order to achieve three supporting tasks: short-term frequency regulation, oscillation damping and voltage regulation. The analysis contemplates the effects of different loading conditions, measurement/communication time delays and control loop gains. Bifurcation diagrams, eigenvalue analysis and nonlinear time-domain simulations are used to assess the power system dynamics. The main contribution of this work is the assessment of wind farm ancillary services on the bifurcation structure of the power system. [ABSTRACT FROM AUTHOR]

The previously developed eigenvalue method for computing the size effect of cohesive crack model is extended to the cohesive crack model with a finite residual stress. In this model, the structure size for which a specified relative length of kink-band corresponds to the maximum load is obtained as an eigenvalue of a homogeneous Fredholm integral equation. This new method is direct and much more efficient than the classical finite element approach in which the entire load-deflection history must be computed to obtain the maximum load. A secondary purpose of the paper is to apply the new method to the effect of structure size on the compressive strength of unidirectional fiber–polymer composites failing by propagation of kink-band with fiber microbuckling. The kink-band is simulated by a cohesive crack model with a linear compressive softening law and a finite residual stress. The simulation shows that the specimens tested have a negative–positive geometry, i.e., the energy release rate of the kink-band for a unit load first decreases but at a certain length of propagation begins to increase. Finally the effect of shape of the softening law of cohesive crack on the size effect curve is studied by using the new eigenvalue method. It is shown that, for a negative–positive geometry, the size effect on the peak load depends on the entire softening curve if the specimens is not too small. [Copyright &y& Elsevier]

The natural trajectory tracking problem is studied for generic quantum states represented by density operators. A control design based on the Hilbert-Schmidt distance as a Lyapunov function is considered. The control dynamics is redefined on an extended space where the LaSalle invariance principle can be correctly applied even for non-stationary target states. LaSalle's invariance principle is used to derive a general characterization of the invariant set, which is shown to always contain the critical points of the Lyapunov function. Critical point analysis of the latter is used to show that, for generic states, it is a Morse function with n! isolated critical points, including one global minimum, one global maximum and n!-2 saddles. It is also shown, however, that the actual dynamics of the system is not a gradient flow, and therefore a full eigenvalue analysis of the linearized dynamics about the critical points of the dynamical system is necessary to ascertain stability of the critical points. This analysis shows that a generic target state is locally asymptotically stable if the linearized system is controllable and the invariant set is regular, and in fact convergence to the target state (trajectory) in this case is almost global in that the stable manifolds of all other critical points form a subset of measure zero of the state space. On the other hand, if either of these sufficient conditions is not satisfied, the target state ceases to be asymptotically stable, a center manifold emerges around the target state, and the control design ceases to be effective. [ABSTRACT FROM PUBLISHER]