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Applied Mathematics Theses and Dissertations

Theses and Dissertations for the Applied Mathematics department.

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Items (1-12) out of 12 results

Boundary Layers for 2D Stationary Navier-Stokes Flows over a Moving Boundary

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
Full Record

Diffusive limit of the Boltzmann equation with boundary conditions

Description:
The derivation of fluid equations from the Boltzmann equation is a fundamental problem in kinetic theory. In this paper, we investigate several results concerning the …
Year:
2025
Contributor:
Jung, Junhwa (creator)
Guo, Yan (Advisor)
Dong, Hongjie (Reader)
Pausader, Benoit (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Differential equations, Partial
Hydrodynamic limit
Kinetic theory of gases
Collection:
Applied Mathematics
Theses and Dissertations
Available to Brown-affiliated users only
Full Record

Homoclinic Snaking of Spatiotemporal Patterns in Reaction Diffusion Systems

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
Full Record

Localized Structures in the Multi-dimensional Swift-Hohenberg Equation

Description:
This goal of this thesis is to understand patterns in the Swift{Hohenberg equation. Thepatterns studied are localized, stationary and radially symmetric in dimensions one throughthree. …
Year:
2011
Contributor:
McCalla, Scott G (creator)
Sandstede, Bjorn (Director)
Mallet-Paret, John (Reader)
Scheel, Arnd (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
Pattern Formation
PDEs
Differential equations, Partial
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Modeling Intracellular Transport during Messenger RNA Localization in Xenopus Oocytes

Description:
Many organisms need to establish spatial orientation during early development. In egg cells (oocytes) of the frog Xenopus laevis, spatial differentiation is achieved by localization …
Year:
2017
Contributor:
Ciocanel, Maria-Veronica (creator)
Sandstede, Bjorn (Advisor)
Maxey, Martin (Reader)
McKinley, Scott (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Developmental biology
Differential equations, Partial
mathematical modelling
Dynamics
Xenopus laevis
Fluorescence microscopy
Parameter estimation
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Multiple Timescales in the Fitzhugh-Nagumo Model

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
Full Record

Small surface tension, infinite time, and light electrons: three results on the asymptotic analysis of PDEs

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
Full Record

Stability and instability in the Stefan problem with surface tension

Description:
We develop a high-order nonlinear energy method to study the stability of steady states of the Stefan problem with surface tension. There are two prominent …
Year:
2010
Contributor:
Hadzic, Mahir (creator)
Guo, Yan (Director)
Dafermos, Constantine (Reader)
Strauss, Walter (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
partial differential equations
Stefan problem
phase transitions
energy method
Differential equations, Partial
Phase transformations (Statistical physics)
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Stratified and steady periodic water waves

Description:
This thesis considers two-dimensional stratified water waves propagating under the force of gravity over an impermeable flat bed and with a free surface. In the …
Year:
2010
Contributor:
Walsh, Samuel Peter (creator)
Strauss, Walter (Director)
Dafermos, Constantine (Reader)
Mallet-Paret, John (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
partial differential equations
elliptic equations
Water waves
Differential equations, Partial
Bifurcation theory
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

The Incompressible Navier-Stokes Equations: Two Regularity Criteria

Description:
This dissertation presents new regularity criteria of the incompressible Navier-Stokes equations and derive further results, including extensions of the Ladyzhenskaya-Prodi-Serrin condition in high dimensional critical …
Year:
2020
Contributor:
Wang, Kunrui (creator)
Dong, Hongjie (Advisor)
Shu, Chi-Wang (Advisor)
Guo, Yan (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Differential equations, Partial
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Theory, Algorithms, and Software for Physics-Informed Deep Learning

Description:
This dissertation is centered around the broad topic of physics-informed deep learning (DL). Specifically, it covers the following three fronts: Algorithms. Recent developments of DL, …
Year:
2020
Contributor:
Lu, Lu (creator)
Karniadakis, George (Advisor)
Harrison, Matthew (Reader)
Stinis, Panos (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Differential equations, Partial
Deep Learning
computational physics
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

“A Derivation and Analysis of the N-point Hierarchy For Conservation Laws And Multistable Dynamics with White Noise in the Allen-Cahn Equation

Description:
The first part of this thesis concerns conservation laws subject to random initial conditions. Using a discrete set of values for the solution, one can …
Year:
2017
Contributor:
Caginalp, Carey (creator)
Menon, Govind (Advisor)
Dafermos, Constantine (Reader)
Kaspar, David (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Differential equations, Partial
Stochastics
Probabilities
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Items (1-12) out of 12 results