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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... 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 Interests: Mathematics and Physics
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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... 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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Influence of damping on hyperbolic equations with parabolic degeneracy
In [20], we derived representation formulae for spatially peri-odic solutions to the generalized, inviscid Proudman-Johnson equation and studied their regularity for several classes of initial data. The pur-pose of this paper is to extend... more
In [20], we derived representation formulae for spatially peri-odic solutions to the generalized, inviscid Proudman-Johnson equation and studied their regularity for several classes of initial data. The pur-pose of this paper is to extend these results to larger classes of functions including those having arbitrary local curvature near particular points in the domain.
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Abstract. We examine periodic solutions to an initial boundary value problem for a Liouville equation with sign-changing weight. A represen-tation formula is derived both for singular and nonsingular boundary data, including data arising... more
Abstract. We examine periodic solutions to an initial boundary value problem for a Liouville equation with sign-changing weight. A represen-tation formula is derived both for singular and nonsingular boundary data, including data arising from fractional linear maps. In the case of singular boundary data we study the effects the induced singularity has on the interior regularity of solutions. Regularity criteria are also found for a generalized form of the equation.
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We analyze nite time singularity formation for two systems of hyper-bolic equations. Our results extend previous proofs of breakdown con-cerning 2 2 non-strictly hyperbolic systems to n n systems, and to a situation where, additionally,... more
We analyze nite time singularity formation for two systems of hyper-bolic equations. Our results extend previous proofs of breakdown con-cerning 2 2 non-strictly hyperbolic systems to n n systems, and to a situation where, additionally, the condition of genuine nonlinearity is vio-lated throughout phase space. The systems we consider include as special cases those examined by Keytz and Kranzer and by Serre. They take the form ut + ((u)u)x = 0; where is a scalar-valued function of the n-dimensional vector u, and ut + (u)ux = 0; under the assumption = diag f1; : : : ; ng with i = i(u − ui), where u − ui fu1; : : : ; ui−1; ui+1; : : : ; ung. 1
(Communicated by the associate editor name) Abstract. We study geodesics of the H1 Riemannian metric ∫ 1 〈〈u, v〉 〉 = 〈u(s), v(s) 〉 + α
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This paper provides results on local and global existence for a class of solutions to the Euler equations for an incompressible, inviscid fluid. By considering a class of solutions which exhibits a characteristic growth at infinity we... more
This paper provides results on local and global existence for a class of solutions to the Euler equations for an incompressible, inviscid fluid. By considering a class of solutions which exhibits a characteristic growth at infinity we obtain an initial value problem for a nonlocal equation. We establish local well-posedness in all dimensions and persistence in time of these solutions for three and higher dimensions. We also examine a weaker class of global solutions. 2
Abstract. Classical heat pulse experiments have shown heat to propagate in waves through crystalline materials at temperatures close to absolute zero. With increasing temperature, these waves slow down and finally disappear, to be... more
Abstract. Classical heat pulse experiments have shown heat to propagate in waves through crystalline materials at temperatures close to absolute zero. With increasing temperature, these waves slow down and finally disappear, to be replaced by diffusive heat propagation. Several features surrounding this phenomenon are examined in this work. The model used switches between an internal parameter (or extended thermodynamics) description and a classical (linear or nonlinear) Fourier law setting. This leads to a hyperbolic-parabolic change of type, which allows wavelike features to appear beneath the transition temperature and diffusion above. We examine the region around and immediately below the transition temperature, where dissipative effects are insignificant.
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For arbitrary values of a parameter λ ∈ R, finite-time blow-up of solutions to the generalized, inviscid Proudman-Johnson equation is studied via a direct approach which involves the derivation of repre-sentation formulae for solutions to... more
For arbitrary values of a parameter λ ∈ R, finite-time blow-up of solutions to the generalized, inviscid Proudman-Johnson equation is studied via a direct approach which involves the derivation of repre-sentation formulae for solutions to the problem.
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Travelling-waves for generalized KdV-Burgers equations by H. Chen Some analytical coherent structures of the long-wave equations by S. R. Choudhury Weakly nonlinear elastic plane waves in a cubic crystal by W. Domanski On dynamics of... more
Travelling-waves for generalized KdV-Burgers equations by H. Chen Some analytical coherent structures of the long-wave equations by S. R. Choudhury Weakly nonlinear elastic plane waves in a cubic crystal by W. Domanski On dynamics of exothermic interfaces by M. L. Frankel and V. Roytburd Similarity solutions for granular flows in hoppers by P.-A. Gremaud, J. V. Matthews, and M. Shearer Stability issues in nonisothermal elongational flow by T. Hagen and M. Renardy The damped $P$-system with boundary effects by L. Hsiao and R. Pan Prototypes for nonstrict hyperbolicity in conservation laws by B. L. Keyfitz and C. A. Mora Stability of blow-up patterns for nonlinear wave equations by S. Kichenassamy Slowly decaying solutions of KdV by M. Kovalyov Fractal solutions of the Schrodinger equation by I. Rodnianski Spectral condition for abstract instability by J. Shatah and W. Strauss On approximation of stable and unstable manifolds and the Stokes phenomenon by A. Tovbis A priori bounds in o...
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We consider phase transitions in solids due to heat propagating through crystalline materials at low temperatures. These are considered in a steady state context where, at the transition temperature, the specific heat becomes singular and... more
We consider phase transitions in solids due to heat propagating through crystalline materials at low temperatures. These are considered in a steady state context where, at the transition temperature, the specific heat becomes singular and the heat conductivity has a maximum. Several consequences are found for the heat capacity having finite or infinite jump discontinuities.
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Classical heat pulse experiments have shown heat to propagate in waves through crystalline materials at temperatures close to absolute zero. With increasing temperature, these waves slow down and finally disappear, to be replaced by... more
Classical heat pulse experiments have shown heat to propagate in waves through crystalline materials at temperatures close to absolute zero. With increasing temperature, these waves slow down and finally disappear, to be replaced by diffusive heat propagation. Several features surrounding this phenomenon are examined in this work. The model used switches between an internal parameter (or extended thermodynamics) description and a classical (linear or nonlinear) Fourier law setting. This leads to a hyperbolic-parabolic change of type, which allows wavelike features to appear beneath the transition temperature and diffusion above. We examine the region around and immediately below the transition temperature, where dissipative effects are insignificant.
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For arbitrary values of a parameter λ ∈ R, finite-time blowup of solutions to the generalized, inviscid Proudman-Johnson equation is studied via a direct approach which involves the derivation of representation formulae for solutions to... more
For arbitrary values of a parameter λ ∈ R, finite-time blowup of solutions to the generalized, inviscid Proudman-Johnson equation is studied via a direct approach which involves the derivation of representation formulae for solutions to the problem. Mathematics Subject Classification (2010). 35B44, 35B10, 35B65, 35Q35.
WE DERIVE a physically justifiable model of heat conduction for rigid heat conductors based on a recent approach involving the gradient generalization of an internal state variable. The model accounts for observable phenomena in solid... more
WE DERIVE a physically justifiable model of heat conduction for rigid heat conductors based on a recent approach involving the gradient generalization of an internal state variable. The model accounts for observable phenomena in solid dielectric crystals, related to wave-like conduction of heat in certain ranges of low temperatures and a rapid decay of the speed of thermal waves close to a temperature value V λ , at which the conductivity of the material reaches a peak.
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We analyze nite time singularity formation for two systems of hyperbolic equations. Our results extend previous proofs of breakdown concerning 2 2 non-strictly hyperbolic systems to nn systems, and to a situation where, additionally, the... more
We analyze nite time singularity formation for two systems of hyperbolic equations. Our results extend previous proofs of breakdown concerning 2 2 non-strictly hyperbolic systems to nn systems, and to a situation where, additionally, the condition of genuine nonlinearity is violated throughout phase space. The systems we consider include as special cases those examined by Keytz and Kranzer and by Serre. They take the form ut +( (u )u )x =0 ; where is a scalar-valued function of the n-dimensional vector u ,a nd u t +(u )ux =0 ;
In order to account for low temperature heat propagation phenomena in crystals of sodium fluoride and bismuth, we employ a thermodynamic model for rigid materials involving a vector-field internal state variable. The model is either... more
In order to account for low temperature heat propagation phenomena in crystals of sodium fluoride and bismuth, we employ a thermodynamic model for rigid materials involving a vector-field internal state variable. The model is either wavelike or diffusive, depending on the temperature regime considered.
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Page 1. SIAM J. APPL. MATH. Q1991 Society for Industrial and Applied Mathematics Vol. 51, No. 6, pp. 1498-1521, December 1991 002 DYNAMICS OF DIRECTOR FIELDS* JOHN K. HUNTERt AND RALPH SAXTONt Abstract. ...
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... Solitary-wave interactions in elastic rods. Auteur(s) / Author(s). CLARKSON PA (1) ; LEVEQUE RJ ; SAXTON R. ; Affiliation(s) du ou des auteurs / Author(s) Affiliation(s). (1)Clarkson univ., Potsdam NY 13676, ETATS-UNIS Revue / Journal... more
... Solitary-wave interactions in elastic rods. Auteur(s) / Author(s). CLARKSON PA (1) ; LEVEQUE RJ ; SAXTON R. ; Affiliation(s) du ou des auteurs / Author(s) Affiliation(s). (1)Clarkson univ., Potsdam NY 13676, ETATS-UNIS Revue / Journal Title. ...
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In order to account for low temperature heat propagation phenomena in crystals of sodium ∞uoride and bismuth, we employ a thermodynamic model for rigid ma- terials involving a vector-fleld internal state variable. The model is either... more
In order to account for low temperature heat propagation phenomena in crystals of sodium ∞uoride and bismuth, we employ a thermodynamic model for rigid ma- terials involving a vector-fleld internal state variable. The model is either wavelike or difiusive, depending on the temperature regime considered.