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Publications about 'Uncertainty quantification in PDEs'


G. Hariharan.
Transition to elastic turbulence in channel flows.
PhD thesis,
University of Minnesota,
2020.
Keyword(s): Distributed systems theory,
Computational tools for spatially distributed systems,
Flow modeling and control,
Viscoelastic fluids,
Inputoutput analysis,
Elastic turbulence,
Transition to turbulence,
Uncertainty quantification in PDEs,
Spatiotemporal impulse responses,
Spatiotemporal frequency responses,
Spectral integration method.
[bibtexentry]

B. K. Lieu.
Dynamics and control of Newtonian and viscoelastic fluids.
PhD thesis,
University of Minnesota,
2014.
Keyword(s): Drag reduction,
Controlling the onset of turbulence,
Control of turbulent flows,
Flow modeling and control,
NavierStokes equations,
Spatiallyperiodic systems,
Traveling waves,
Vibrational control,
Distributed systems theory,
Computational tools for spatially distributed systems,
Uncertainty quantification in PDEs,
Viscoelastic fluids,
Inputoutput analysis,
Elastic turbulence,
Transition to turbulence,
Worstcase amplification.
[bibtexentry]

H. A. Castillo,
M. R. Jovanovic,
S. Kumar,
A. Morozov,
V. Shankar,
G. Subramanian,
and H. J. Wilson.
Understanding viscoelastic flow instabilities: OldroydB and beyond.
J. NonNewtonian Fluid Mech.,
302:104742 (39 pages),
April 2022.
Note: Part of the special issue commemorating the birth centenary of James Oldroyd.
Keyword(s): Flow modeling and control,
Inputoutput analysis,
Elastic turbulence,
Energy amplification,
Transition to turbulence,
Uncertainty quantification in PDEs,
Spatiotemporal frequency responses,
Viscoelastic fluids,
Viscoelastic instabilities.
[bibtexentry]

G. Hariharan,
M. R. Jovanovic,
and S. Kumar.
Localized stress amplification in inertialess channel flows of viscoelastic fluids.
J. NonNewtonian Fluid Mech.,
291:104514 (14 pages),
May 2021.
Keyword(s): Flow modeling and control,
Viscoelastic fluids,
Inputoutput analysis,
Elastic turbulence,
Transition to turbulence,
Uncertainty quantification in PDEs,
Spatiotemporal impulse responses.
[bibtexentry]

G. Hariharan,
S. Kumar,
and M. R. Jovanovic.
Wellconditioned ultraspherical and spectral integration methods for resolvent analysis of channel flows of Newtonian and viscoelastic fluids.
J. Comput. Phys.,
439:110241 (25 pages),
August 2021.
Keyword(s): Distributed systems theory,
Computational tools for spatially distributed systems,
Flow modeling and control,
Inputoutput analysis,
Spatiotemporal frequency responses,
Spectral integration method,
Uncertainty quantification in PDEs.
[bibtexentry]

G. Hariharan,
M. R. Jovanovic,
and S. Kumar.
Amplification of localized body forces in channel flows of viscoelastic fluids.
J. NonNewtonian Fluid Mech.,
260:4053,
October 2018.
Keyword(s): Flow modeling and control,
Viscoelastic fluids,
Inputoutput analysis,
Elastic turbulence,
Transition to turbulence,
Uncertainty quantification in PDEs,
Spatiotemporal impulse responses.
[bibtexentry]

B. K. Lieu and M. R. Jovanovic.
Computation of frequency responses for linear timeinvariant PDEs on a compact interval.
J. Comput. Phys.,
250:246269,
October 2013.
Keyword(s): Distributed systems theory,
Computational tools for spatially distributed systems,
Uncertainty quantification in PDEs.
[bibtexentry]

B. K. Lieu,
M. R. Jovanovic,
and S. Kumar.
Worstcase amplification of disturbances in inertialess Couette flow of viscoelastic fluids.
J. Fluid Mech.,
723:232263,
May 2013.
Keyword(s): Flow modeling and control,
Viscoelastic fluids,
Inputoutput analysis,
Elastic turbulence,
Transition to turbulence,
Uncertainty quantification in PDEs,
Worstcase amplification.
[bibtexentry]

S. Y. Shafi,
M. Arcak,
M. R. Jovanovic,
and A. Packard.
Synchronization of diffusivelycoupled limit cycle oscillators.
Automatica,
49(12):36133622,
December 2013.
Keyword(s): Biochemical networks,
Diffusively coupled systems,
Timeperiodic systems,
Synchronization,
Uncertainty quantification in PDEs.
[bibtexentry]

M. Fardad,
M. R. Jovanovic,
and B. Bamieh.
Frequency analysis and norms of distributed spatially periodic systems.
IEEE Trans. Automat. Control,
53(10):22662279,
November 2008.
Keyword(s): Distributed systems theory,
Inputoutput analysis,
Spatiallyperiodic systems,
Uncertainty quantification in PDEs.
[bibtexentry]

M. R. Jovanovic and M. Fardad.
$H_2$ norm of linear timeperiodic systems: a perturbation analysis.
Automatica,
44(8):20902098,
August 2008.
Keyword(s): Distributed systems theory,
Inputoutput analysis,
Timeperiodic systems,
Perturbation analysis,
Uncertainty quantification in PDEs.
[bibtexentry]

M. R. Jovanovic and B. Bamieh.
A formula for frequency responses of distributed systems with one spatial variable.
Syst. Control Lett.,
55(1):2737,
January 2006.
Keyword(s): Distributed systems theory,
Computational tools for spatially distributed systems,
Uncertainty quantification in PDEs.
[bibtexentry]

G. Hariharan,
M. R. Jovanovic,
and S. Kumar.
Spatiotemporal impulse responses in channel flow of viscoelastic fluids.
In Proceedings of the 2018 American Control Conference,
Milwaukee, WI,
pages 28572862,
2018.
Keyword(s): Flow modeling and control,
Viscoelastic fluids,
Inputoutput analysis,
Elastic turbulence,
Transition to turbulence,
Uncertainty quantification in PDEs,
Spatiotemporal impulse responses.
[bibtexentry]

S. Y. Shafi,
M. Arcak,
and M. R. Jovanovic.
Synchronization of limit cycle oscillations in diffusivelycoupled systems.
In Proceedings of the 2013 American Control Conference,
Washington, DC,
pages 48744879,
2013.
Keyword(s): Biochemical networks,
Diffusively coupled systems,
Timeperiodic systems,
Synchronization,
Uncertainty quantification in PDEs.
[bibtexentry]

B. K. Lieu and M. R. Jovanovic.
Computation of the frequency responses for distributed systems with one spatial variable.
In Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference,
Orlando, FL,
pages 69566961,
2011.
Keyword(s): Distributed systems theory,
Computational tools for spatially distributed systems,
Uncertainty quantification in PDEs.
[bibtexentry]

B. K. Lieu,
M. R. Jovanovic,
and S. Kumar.
Worstcase amplification of disturbances in inertialess flows of viscoelastic fluids.
In Preprints of the 18th IFAC World Congress,
Milano, Italy,
pages 1445814463,
2011.
Keyword(s): Flow modeling and control,
Viscoelastic fluids,
Inputoutput analysis,
Elastic turbulence,
Transition to turbulence,
Uncertainty quantification in PDEs,
Worstcase amplification.
[bibtexentry]

M. Fardad,
M. R. Jovanovic,
and M. V. Salapaka.
Damping mechanisms in dynamic mode atomic force microscopy applications.
In Proceedings of the 2009 American Control Conference,
Saint Louis, MO,
pages 22722277,
2009.
Keyword(s): Atomic force microscopy,
Distributed systems theory,
Inputoutput analysis,
Uncertainty quantification in PDEs.
[bibtexentry]
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