Current Search: poster (x) » FAU Graduate Student Research (x) » Kalies, William D. (x)
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Title
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A Local Regression Approach to Computing the Cauchy Green Strain Tensor.
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Creator
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Kepley, Shane, Kalies, William D., Graduate College
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Abstract/Description
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The Cauchy Green strain tensor provides an effective tool for understanding unsteady flows. In particular, the dominant eigenvalue of this tensor has been seen to be a reliable estimator of the finite time Lyapunov exponent. We propose a new method for computing the CG strain tensor using a local quadratic regression LOESS technique. We compare this LOESS method with several classical methods using closed form flows, noisy flows, and simulated time series. In each case, the CG strain tensor...
Show moreThe Cauchy Green strain tensor provides an effective tool for understanding unsteady flows. In particular, the dominant eigenvalue of this tensor has been seen to be a reliable estimator of the finite time Lyapunov exponent. We propose a new method for computing the CG strain tensor using a local quadratic regression LOESS technique. We compare this LOESS method with several classical methods using closed form flows, noisy flows, and simulated time series. In each case, the CG strain tensor produced by the LOESS method is remarkably accurate and robust compared to classical methods.
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Date Issued
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2015
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PURL
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http://purl.flvc.org/fau/fd/FA00005890
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Format
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Document (PDF)
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Title
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A computational approach analyzing global dynamics.
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Creator
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Kasti, Dinesh, Van der Vorst, R.C.A.M., Kalies, William D., Graduate College
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Abstract/Description
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We describe the lattice structure of attractors in a dynamical system and the lifting of sublattices of attractors, which are computationally less accessible, to lattices of forward invariant sets and attracting neighborhoods, which are computationally accessible. We also show how the use of these algebraic structures of lattices to help us to capture the information about underlying dynamical system in a more elegant way and with lesser computational cost. For example, they can be used to...
Show moreWe describe the lattice structure of attractors in a dynamical system and the lifting of sublattices of attractors, which are computationally less accessible, to lattices of forward invariant sets and attracting neighborhoods, which are computationally accessible. We also show how the use of these algebraic structures of lattices to help us to capture the information about underlying dynamical system in a more elegant way and with lesser computational cost. For example, they can be used to develop a much efficient algorithm to compute a global lyapunov function that describes the overall gradient dynamics.
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Date Issued
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2015
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PURL
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http://purl.flvc.org/fau/fd/FA00005888
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Format
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Document (PDF)
