Current Search: Kepley, Shane (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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The Circular Restricted Four Body Problem is Non-Integrable: A Computer Assisted Proof.
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Creator
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Kepley, Shane, Kalies, William D., Mireles-James, Jason D., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
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Abstract/Description
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Gravitational N-body problems are central in classical mathematical physics. Studying their long time behavior raises subtle questions about the interplay between regular and irregular motions and the boundary between integrable and chaotic dynamics. Over the last hundred years, concepts from the qualitative theory of dynamical systems such as stable/unstable manifolds, homoclinic and heteroclinic tangles, KAM theory, and whiskered invariant tori, have come to play an increasingly important...
Show moreGravitational N-body problems are central in classical mathematical physics. Studying their long time behavior raises subtle questions about the interplay between regular and irregular motions and the boundary between integrable and chaotic dynamics. Over the last hundred years, concepts from the qualitative theory of dynamical systems such as stable/unstable manifolds, homoclinic and heteroclinic tangles, KAM theory, and whiskered invariant tori, have come to play an increasingly important role in the discussion. In the last fty years the study of numerical methods for computing invariant objects has matured into a thriving sub-discipline. This growth is driven at least in part by the needs of the world's space programs. Recent work on validated numerical methods has begun to unify the computational and analytical perspectives, enriching both aspects of the subject. Many of these results use computer assisted proofs, a tool which has become increasingly popular in recent years. This thesis presents a proof that the circular restricted four body problem is non-integrable. The proof of this result is obtained as an application of more general rigorous numerical methods in nonlinear analysis.
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Date Issued
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2017
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PURL
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http://purl.flvc.org/fau/fd/FA00004997
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Subject Headings
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Dissertations, Academic -- Florida Atlantic University, Mathematical physics., Invariants., Dynamical systems
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Format
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Document (PDF)
