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Full-Text Articles in Mathematics
Slow Flow Between Concentric Cones, O. Hall, C. P. Hills, A. D. Gilbert
Slow Flow Between Concentric Cones, O. Hall, C. P. Hills, A. D. Gilbert
Articles
This paper considers the low-Reynolds-number flow of an incompressible fluid contained in the gap between two coaxial cones with coincident apices and bounded by a spherical lid. The two cones and the lid are allowed to rotate independently about their common axis, generating a swirling motion. The swirl induces a secondary, meridional circulation through inertial effects. For specific configurations complex eigenmodes representing an infinite sequence of eddies, analogous to those found in two-dimensional corner flows and some three-dimensional geometries, form a component of this secondary circulation. When the cones rotate these eigenmodes, arising from the geometry, compete with the forced …
Krylov Subspaces From Bilinear Representations Of Nonlinear Systems, Marissa Condon, Rossen Ivanov
Krylov Subspaces From Bilinear Representations Of Nonlinear Systems, Marissa Condon, Rossen Ivanov
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For efficient simulation of state-of-the-art dynamical systems as arise in all aspects of engineering, the development of reduced-order models is of paramount importance. While linear reduction techniques have received considerable study, increasingly nonlinear model reduction is becoming a significant field of interest. From a circuits and systems viewpoint, systems involving micromachined devices or systems involving mixed technologies necessitate the development of reduced-order nonlinear models. From a control systems viewpoint, the design of controllers for nonlinear systems is greatly facilitated by nonlinear model reduction strategies. To this end, the paper proposes two novel model-reduction strategies for nonlinear systems. The first involves …