Solitary waves and nonlinear Klein-Gordon Equations

We analytically study the kink-antikink (K-K) collisions in the classical one spatial dimension and time phi-fourth field theory as an example of inelastic collisions between solitary waves. We use the linear eigenvalue collective coordinate approach to describe the system in terms of the separation distance between the kink and the antikink and the amplitude of shape vibrations generated on each kink as a result of the collision. By calculating the energy given to the shape vibrations as a function of the incoming velocity, we find the critical value of the initial velocity above which the two colliding kinks always separate after the collision. A model previously proposed to explain the two-bounce collisions in terms of a resonant energy exchange between the orbital frequency of the bound K-K pair and the frequency of shape vibrations is modified using our analytical results. We derive a (data-free) formula that predicts the values of the initial velocities for which resonance occurs. A generalized version of this modified model is shown to give good results when it is applied to K-K collisions in other similar field theories. In the Appendices Nonlinear Klein Gordon equations with solitary (travelling) wave solutions are reviewed and solved for particular cases. The solutions are related to soliton solutions of the sine-Gordon equation. Also the phi-fourth equation perturbed with a constant force and dissipation is solved, and finally, we present new kink-bearing integro-differential and nonlinear differential equations

Incomplete Orthogonal Factorization Methods Using Givens Rotations II: Implementation and Results

We present, implement and test a series of incomplete orthogonal factorization methods based on Givens rotations for large sparse unsymmetric matrices. These methods include: column-Incomplete Givens Orthogonalization (cIGO-method), which drops entries by position only; column-Threshold Incomplete Givens Orthogonalization (cTIGO-method) which drops entries dynamically by both their magnitudes and positions and where the reduction via Givens rotations is done in a column-wise fashion; and, row-Threshold Incomplete Givens Orthogonalization (r-TIGO-method) which again drops entries dynamically, but only magnitude is now taken into account and reduction is performed in a row-wise fashion. We give comprehensive accounts of how one would code these algorithms using a high level language to ensure efficiency of computation and memory use. The methods are then applied to a variety of square systems and their performance as preconditioners is tested against standard incomplete LU factorization techniques. For rectangular matrices corresponding to least-squares problems, the resulting incomplete factorizations are applied as preconditioners for conjugate gradients for the system of normal equations. A comprehensive discussion about the uses, advantages and shortcomings of these preconditioners is given

Measurement based method for online characterization of generator dynamic behaviour in systems with renewable generation

This paper introduces a hybrid-methodology for online identification and clustering of generator oscillatory behavior, based on measured responses. The dominant modes in generator measured responses are initially identified using a mode identification technique and then introduced, in the next step, as input into a clustering algorithm. Critical groups of generators that exhibit poorly or negatively damped oscillations are identified, in order to enable corrective control actions and stabilize the system. The uncertainties associated with operation of modern power systems, including Renewable Energy Sources (RES) are investigated, with emphasis on the impact of the dynamic behavior of power electronic interfaced RES

Engineering failure analysis and design optimisation with HiP-HOPS

The scale and complexity of computer-based safety critical systems, like those used in the transport and manufacturing industries, pose significant challenges for failure analysis. Over the last decade, research has focused on automating this task. In one approach, predictive models of system failure are constructed from the topology of the system and local component failure models using a process of composition. An alternative approach employs model-checking of state automata to study the effects of failure and verify system safety properties. In this paper, we discuss these two approaches to failure analysis. We then focus on Hierarchically Performed Hazard Origin & Propagation Studies (HiP-HOPS) - one of the more advanced compositional approaches - and discuss its capabilities for automatic synthesis of fault trees, combinatorial Failure Modes and Effects Analyses, and reliability versus cost optimisation of systems via application of automatic model transformations. We summarise these contributions and demonstrate the application of HiP-HOPS on a simplified fuel oil system for a ship engine. In light of this example, we discuss strengths and limitations of the method in relation to other state-of-the-art techniques. In particular, because HiP-HOPS is deductive in nature, relating system failures back to their causes, it is less prone to combinatorial explosion and can more readily be iterated. For this reason, it enables exhaustive assessment of combinations of failures and design optimisation using computationally expensive meta-heuristics. (C) 2010 Elsevier Ltd. All rights reserved