This paper deals with a normal form of a class of nonlinear dynamical systems. This form enables us to design a reduced-order observer for a class of nonlinear dynamical system. Necessary and sufficient geometrical conditions for the existence of a coordinate change to transform a given singular dynamical system into such normal form are also given.

phase turbulence, but underpredict the two-phase fluctuation velocities, and the difference between the two model predictions is not obvious. 4. The nonlinear k-«-kp model has no problem of convergence encountered in the implicit algebraic stress model. 5. In two-dimensional flows with small geometrical sizes the NKP model can save about 50% computation time than the USM model. However, in thre...

A powerful method to solve nonlinear first-order ordinary differential equations, which is based on a geometrical understanding of the corresponding dynamics of the so-called Lie systems, is developed. This method enables us not only to solve some of these equations, but also gives geometrical explanations for some, already known, ad hoc methods of dealing with such problems. MSC 2000: 34A26 (P...

This tutorial provides a nonlinear dynamics perspective to Wolfram’s monumental work on A New Kind of Science. By mapping a Boolean local Rule, or truth table, onto the point attractors of a specially tailored nonlinear dynamical system, we show how some of Wolfram’s empirical observations can be justified on firm ground. The advantage of this new approach for studying Cellular Automata phenome...

Hyperelastic materials based on Signorini’s strain energy density are studied by using Shannon wavelets. Cylindrical waves propagating in a nonlinear elastic material from the circular cylindrical cavity along the radius are analyzed in the following by focusing both on the main nonlinear effects and on the method of solution for the corresponding nonlinear differential equation. Cylindrical wa...

We analyse the dynamical behaviour of a harmonically excited piezoceramic in dependence on certain design parameters. In particular, we explore its dynamics in dependence on its geometrical shape as well as the influence of nonlinear terms in the associated equations of motion. First we derive a two point boundary value problem whose solutions yield certain eigenfunctions of the linearized mode...

Many processes in science and engineering develop multiscale temporal and spatial patterns, with complex underlying dynamics and time-dependent external forcings. Because of the importance in understanding and predicting these phenomena, extracting the salient modes of variability empirically from incomplete observations is a problem of wide contemporary interest. Here, we present a technique f...

| In this paper design sensitivity analysis is applied to solve the TEAM workshop problem 25. In order to justify the use of a gradient method, it is necessary to assume a continuously di erentiable dependence of the sti ness matrix on the design parameters. Since design sensitivity analysis is mainly applicable to optimization problems, where the geometrical parameters undergo small changes on...

The paper presents a comparative assessment of Blind Source Separation (BSS) methods for instantaneous mixtures based on namely generalized eigen-value decomposition, geometrical concepts, differential of mutual information and Kalman filtering applied to Nonlinear Principal Component Analysis (Nonlinear PCA). The methods highlight the independence concept underlying Independent Component Analy...