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An analysis of the Lagrangian motion for small particles denser than surrounding fluid in a two-dimensional steady cellular flow is presented. The Stokes drag, fluid acceleration, and added mass effect are included in the particle equation of motion. Although the fluid motion is regular, the particle motion can be either chaotic or regular depending on the Stokes number and density ratio. The implications of chaotic motion to particle mixing and dispersion are discussed. Chaotic orbits lead to the dispersion of particle clouds which has many of the features of turbulent dispersion. The mixing process of particles is greatly enhanced since the chaotic advection has the property of ergodicity. However, a high dispersion rate was found to be correlated with low fractal dimension and low mixing efficiency. A similar correlation between dispersion and mixing was found for particles convected by a plane shear mixing layer.

The authors analyze the problem of model reduction in structural dynamics for unforced conser vative systems having static, cubic nonlinearities. The framework is the classical one of partitioning the coordinate vector into subsets of so-called master and slave coordinates, with the reduced dynamic model to contain only the masters. The objective is to compare the quality of two model-reduction methods: (1) a re duction based on the leading order calculation of the nonlinear master-slave state transformation defining the manifold containing the modes to be represented in the reduced model ("NNM-based reduction") and (2) a "linear-based reduction" utilizing the exact for the linear case master-slave state transformation; the linear- based reduction is equivalent to a modal analysis, but the reduced model is defined in terms of the physical, rather than the modal, coordinates. For the simple, low-order oscillator systems considered as examples, the authors have found the NNM-based reduction, which one would expect to be superior, to suffer degradation in quality in the presence of near (and not so near) three to one internal resonance conditions. The linear-based reduction is much simpler to implement and seems to provide competitive results over wide ranges in the system parameters. This conclusion may not carry over to other, higher degree-of-freedom systems.

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