By introducing the second order Krylov subspace, a method for the reduction of second order systems is proposed leading to a reduced system of the same structure. This generalization of Krylov subspace involves two matrices and some starting vectors and the reduced order model is found by applying a projection directly to the second order model without any conversion to state space. A numerical...

Abstract—Slope stability analyses are largely carried out by deterministic methods and evaluated through a single security factor. Although it is known that the geotechnical parameters can present great dispersal, such analyses are considered fixed and known. The probabilistic methods, in turn, incorporate the variability of input key parameters (random variables), resulting in a range of value...

An accurate evaluation of the structural performance of reinforced concrete structural systems under seismic loading requires a probabilistic approach due to uncertainties in structural properties and the ground motion (referred to as basic uncertainties). The objective of this study is to identify and rank significant sources of basic uncertainties and structural components with respect to the...

The second moment method has been fruitfully combined with conditioning by several authors, for example Robinson and Wormald 7], 8] and Frieze and Janson 2]. We try to give a general exposition of this method, and of its relation to approximations of random variables by simpler variables. We discuss several examples where the method has been used in diierent forms. 1. The second moment method O...

It is now generally accepted that statistical turbulence models are unlikely, ever, to enable highfidelity predictions of massively-separated flows, especially if separation occurs from curved three-dimensional surfaces. In such circumstances, even the most elaborate turbulence models are ill-equipped to capture the dynamics associated with highly-unsteady and intense large-scale motions that a...

Heinz von Foerster proposed that the observer should be included in the domain of observation. He suggested that this approach to cybernetics be called second-order cybernetics. Heinz was primarily interested in understanding cognition, based on neurophysiology and mathematics. But there has also been strong interest in cybernetics as a theory of social systems. Using the “second order” idea fo...