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Papers by Ralph Saxton

Research paper thumbnail of Dynamic Modeling of Flow Induced Vibration Power-Plants

Volume 10: Ocean Renewable Energy, 2018

Based on experimental data from the Marine Renewable Energy Laboratory (MRELab) at the University... more Based on experimental data from the Marine Renewable Energy Laboratory (MRELab) at the University of Michigan, a data model is developed in order to permit dynamical analysis and controller synthesis for power-plants based on Vortex Induced Vibrations (VIV) for power generation and energy production. For the particular experimental settings used at the MRELab, data series of various kinematic, dynamic and energetic variables were recorded through the use of one to two cylinders as bluff bodies in a cross-flow. In the present research, these data series are analyzed in order to produce a dynamical model in an appropriate phase space. The process of model derivation is entirely data-driven in the sense that the number of degrees of freedom, or state variables, reflects the dimension of the phase space for the process. The outcome is a model which allows the identification of regime-dependent features such as attractors, basins of attraction, separatrices, etc., which can occur in the ...

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Research paper thumbnail of A sign-changing Liouville equation

Journal of Evolution Equations, May 23, 2015

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Research paper thumbnail of Phase Transitions and Change of Type in Low-Temperature Heat Propagation

Siam Journal on Applied Mathematics, 2006

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Research paper thumbnail of Global Existence of Some Infinite Energy Solutions for a Perfect Incompressible Fluid

Siam Journal on Mathematical Analysis, 2008

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Research paper thumbnail of The role of initial curvature in solutions to the generalized inviscid Proudman-Johnson equation

Quarterly of Applied Mathematics, Jan 21, 2015

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Research paper thumbnail of On second sound at the critical temperature

Quarterly of Applied Mathematics, Dec 1, 1999

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Research paper thumbnail of Existence of solutions for a finite nonlinearly hyperelastic rod

Journal of Mathematical Analysis and Applications, 1985

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Research paper thumbnail of The initial-value problem for elastodynamics of incompressible bodies

Archive for Rational Mechanics and Analysis, 1986

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Research paper thumbnail of Solitary-Wave Interactions in Elastic Rods

Studies in Applied Mathematics, Oct 1, 1986

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Research paper thumbnail of Solitary and travelling waves in a rod

Lecture Notes in Mathematics, 1982

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Research paper thumbnail of On the influence of damping in hyperbolic equations with parabolic degeneracy

Quarterly of Applied Mathematics, Aug 29, 2011

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Research paper thumbnail of Phase Transitions and Aspects of Heat Propagation in Low Temperature Solids

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Research paper thumbnail of Dynamic instability of the liquid crystal director

Contemporary mathematics, 1989

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Research paper thumbnail of Influence of damping on hyperbolic equations with parabolic degeneracy

Quarterly of Applied Mathematics, 2012

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Research paper thumbnail of Global Existence of Infinite Energy Solutions for a Perfect Incompressible Fluid

arXiv (Cornell University), Aug 27, 2006

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Research paper thumbnail of Formation of singularities for a class of nonlinear, hyperbolically degenerate initial-boundary value problems

Applied Mathematics Letters, May 1, 1992

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Research paper thumbnail of Nonlinearity and memory effects in low temperature heat propagation

Archives of Mechanics, 2000

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Research paper thumbnail of The nonlinear Pochhammer-Chree problem

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Research paper thumbnail of Thermal waves, second sound - work of Witold Kosiński

Mathematica Applicanda, Jan 26, 2016

This paper is dedicated to Witold Kosinski. Our contribution to this special issue will concentra... more This paper is dedicated to Witold Kosinski. Our contribution to this special issue will concentrate on the properties of thermal waves, one of many scientic interests of our friend and collaborator, and this article is dedicated to his memory. Working together with Witold was always an insightful and very pleasant experience, and it beneted all of his coworkers including the authors of this note. His scope of research was broad, spanning many disciplines and applications. Here we focus on a few of those aspects to which he applied a deep knowledge of continuum thermodynamics and its mathematical foundations.

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Research paper thumbnail of Singularity formation in systems of non-strictly hyperbolic equations

DOAJ (DOAJ: Directory of Open Access Journals), Jun 1, 1995

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Research paper thumbnail of Dynamic Modeling of Flow Induced Vibration Power-Plants

Volume 10: Ocean Renewable Energy, 2018

Based on experimental data from the Marine Renewable Energy Laboratory (MRELab) at the University... more Based on experimental data from the Marine Renewable Energy Laboratory (MRELab) at the University of Michigan, a data model is developed in order to permit dynamical analysis and controller synthesis for power-plants based on Vortex Induced Vibrations (VIV) for power generation and energy production. For the particular experimental settings used at the MRELab, data series of various kinematic, dynamic and energetic variables were recorded through the use of one to two cylinders as bluff bodies in a cross-flow. In the present research, these data series are analyzed in order to produce a dynamical model in an appropriate phase space. The process of model derivation is entirely data-driven in the sense that the number of degrees of freedom, or state variables, reflects the dimension of the phase space for the process. The outcome is a model which allows the identification of regime-dependent features such as attractors, basins of attraction, separatrices, etc., which can occur in the ...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of A sign-changing Liouville equation

Journal of Evolution Equations, May 23, 2015

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Phase Transitions and Change of Type in Low-Temperature Heat Propagation

Siam Journal on Applied Mathematics, 2006

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Global Existence of Some Infinite Energy Solutions for a Perfect Incompressible Fluid

Siam Journal on Mathematical Analysis, 2008

Bookmarks Related papers MentionsView impact

Research paper thumbnail of The role of initial curvature in solutions to the generalized inviscid Proudman-Johnson equation

Quarterly of Applied Mathematics, Jan 21, 2015

Bookmarks Related papers MentionsView impact

Research paper thumbnail of On second sound at the critical temperature

Quarterly of Applied Mathematics, Dec 1, 1999

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Existence of solutions for a finite nonlinearly hyperelastic rod

Journal of Mathematical Analysis and Applications, 1985

Bookmarks Related papers MentionsView impact

Research paper thumbnail of The initial-value problem for elastodynamics of incompressible bodies

Archive for Rational Mechanics and Analysis, 1986

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Solitary-Wave Interactions in Elastic Rods

Studies in Applied Mathematics, Oct 1, 1986

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Solitary and travelling waves in a rod

Lecture Notes in Mathematics, 1982

Bookmarks Related papers MentionsView impact

Research paper thumbnail of On the influence of damping in hyperbolic equations with parabolic degeneracy

Quarterly of Applied Mathematics, Aug 29, 2011

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Phase Transitions and Aspects of Heat Propagation in Low Temperature Solids

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Dynamic instability of the liquid crystal director

Contemporary mathematics, 1989

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Influence of damping on hyperbolic equations with parabolic degeneracy

Quarterly of Applied Mathematics, 2012

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Global Existence of Infinite Energy Solutions for a Perfect Incompressible Fluid

arXiv (Cornell University), Aug 27, 2006

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Formation of singularities for a class of nonlinear, hyperbolically degenerate initial-boundary value problems

Applied Mathematics Letters, May 1, 1992

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Nonlinearity and memory effects in low temperature heat propagation

Archives of Mechanics, 2000

Bookmarks Related papers MentionsView impact

Research paper thumbnail of The nonlinear Pochhammer-Chree problem

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Thermal waves, second sound - work of Witold Kosiński

Mathematica Applicanda, Jan 26, 2016

This paper is dedicated to Witold Kosinski. Our contribution to this special issue will concentra... more This paper is dedicated to Witold Kosinski. Our contribution to this special issue will concentrate on the properties of thermal waves, one of many scientic interests of our friend and collaborator, and this article is dedicated to his memory. Working together with Witold was always an insightful and very pleasant experience, and it beneted all of his coworkers including the authors of this note. His scope of research was broad, spanning many disciplines and applications. Here we focus on a few of those aspects to which he applied a deep knowledge of continuum thermodynamics and its mathematical foundations.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Singularity formation in systems of non-strictly hyperbolic equations

DOAJ (DOAJ: Directory of Open Access Journals), Jun 1, 1995

Bookmarks Related papers MentionsView impact

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