Applied Mathematics Theses and Dissertations

Theses and Dissertations for the Applied Mathematics department.

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Description:: In this thesis, we study Prandtl's boundary layer theory for 2D, stationary, incompressible Navier-Stokes flows posed on domains with boundaries. The boundary layer hypothesis posed …
Year:: 2018
Contributor:: Iyer, Sameer S. (creator); Guo, Yan (Advisor); Menon, Govind (Reader); Pausader, Benoit (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: Differential equations, Partial; Fluid mechanics; Boundary layer
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: Spatially localized structures, in which a spatially oscillatory pattern on a finite spatial range connects to a trivial homogeneous solution outside this range, have been …
Year:: 2015
Contributor:: Makrides, Elizabeth (creator); Sandstede, Bjorn (Director); Beck, Margaret (Reader); Menon, Govind (Reader); Brown University. Applied Mathematics (sponsor)
Genre:: theses
Subject:: dynamical systems; pattern formation; PDEs; spatial dynamics; Evans function; Dynamics; Pattern formation (Physical sciences)
Language:: English
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: Abstract of Homoclinic Snaking of Spatiotemporal Patterns in Reaction Diffusion Equations, by Timothy V Roberts, Ph.D., Brown University, May 2024. Spiral and target waves are …
Year:: 2024
Contributor:: Roberts, Timothy Victor (creator); Sandstede, Bjorn (Advisor); Beck, Margaret (Reader); Menon, Govind (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: Differential equations, Partial; Applied mathematics; Pattern formation (Biology); dynamical systems
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: In this thesis, we study kinetics and the folding of RNAs and other polymers. In the first part, we study the problem from a statistical …
Year:: 2019
Contributor:: Zhou, Guangyao (creator); Geman, Stuart (Advisor); Lawrence, Charles (Reader); Menon, Govind (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: RNA; Protein folding; Molecular dynamics; entropic barriers
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: Abstract of Multiple Timescales in the Fitzhugh-Nagumo Model, by Erik Bergland, Ph.D., Brown University, October 2024. In addition to its importance to the field of …
Year:: 2024
Contributor:: Bergland, Erik (creator); Sandstede, Bjorn (Advisor); Menon, Govind (Reader); Carter, Paul (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: Differential equations, Partial; Geometric Singular Perturbation Theory; Ordinary Differential Equations; Mathematical analysis
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: Oscillons are spatially localized, time-periodic structures that have been observed in many natural processes, often under temporally periodic forcing. Near Hopf bifurcations, such systems can …
Year:: 2014
Contributor:: McQuighan, Kelly Teresa (creator); Sandstede, Bjorn (Director); Menon, Govind (Reader); Dafermos, Constantine (Reader); Brown University. Applied Mathematics (sponsor)
Genre:: theses
Subject:: dynamical systems; pattern formation; oscillons; spatial dynamics; localized radial structures; geometric blow-up; complex Ginzburg--Landau equation; Dynamics
Language:: English
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: We investigate two different topics in discrete mathematics: the geometry of piecewise-linear surfaces and the long-term behavior of discrete dynamical systems. A regular polygon surface …
Year:: 2018
Contributor:: Alevy, Ian (creator); Kenyon, Richard (Advisor); Menon, Govind (Reader); Schwartz, Richard (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: Dynamics; Probability; Discrete mathematics; Geometry; Statistical mechanics
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: This thesis is an anthology of three works, which each deal with the rigorous justification of a limit of a nonlinear PDE from kinetic theory …
Year:: 2023
Contributor:: Flynn, Patrick (creator); Menon, Govind (Reader); Pausader, Benoit (Advisor); Gomez Serrano, Javier (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: Differential equations, Partial; Fluids; Harmonic analysis; Kinetic theory of gases
Collection:: Applied Mathematics; Theses and Dissertations

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