This paper suggests a procedure for estimating excursion probabilities for linear and nonlinear systems subjected to Gaussian excitation processes. The stochastic excitation process is modeled most generally by the Karhunen-Loève expansion. The approach is based on the so called “averaged excursion probability flow” which allows for a simple solution for the interaction in excursion problems. S...

A numerical method for constructing non-linear normal modes (NNMs) for piecewise linear autonomous systems is presented. These NNMs are based on the concept of invariant manifolds, and are obtained using a Galerkin-based solution of the invariant manifold’s non-linear partial differential equations. The accuracy of the constructed non-linear modes is checked by the comparison of the motion on t...

The measurability by means of continuous measurements, of an observable A(t0), at an instant, and of a time averaged observable, Ā = 1/T ∫ A(t)dt, is examined for linear and in particular for non-linear quantum mechanical systems. We argue that only when the exact (non-perturbative) solution is known, an exact measurement may be possible. A perturbative approach is shown to fail in the non-line...

A new non-linear method for design and analysis of solid state power amplifiers is presented and applied to an aluminum gallium nitride, gallium nitride (AlGaN-GaN) high electron-mobility transistor (HEMTs) on silicon-carbide (SiC) substrate for Ku band (12.4 13.6 GHz) applications. With combining output power of 8 transistors, maximum output power of 46.3 dBm (42.6 W), PAE of 43% and linear ga...

the concept of land use transition highlights that land use change is non-linear and is associated with other societal and biophysical system changes. changes in human systems has resulted in changes in the natural system such as changes in land use. land use change causes not only environmental factors like geography and topography are important, but social factors examined such as population ...