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Applied Mathematics Theses and Dissertations

Theses and Dissertations for the Applied Mathematics department.

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  • 13 2022

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Items (1-13) out of 13 results

Analysis and Implementation of Some Stabilized Finite Element Methods Applied to Fluid Mechanics

Description:
In this dissertation we propose, analyze and computationally implement finite element models to two different two-dimensional saddle point systems of partial differential equations with boundary …
Year:
2022
Contributor:
Cáceres-Valenzuela, Ernesto David (creator)
Guzmán, Johnny (Advisor)
Shu, Chi-Wang (Reader)
Barrenechea, Gabriel (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Finite element method
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Brownian motion on homogeneous space and control systems via Riemannian submersion using mean curvature drift

Description:
We begin by asking how to write down Brownian motion on certain quotient Riemannian manifolds. The projection formula for the Laplace-Beltrami operator through Riemannian submersions …
Year:
2022
Contributor:
Huang, Ching-Peng (creator)
Hassett, Brendan (Reader)
Menon, Govind (Advisor)
Darbon, Jérôme (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Stochastic processes
Geometry, Riemannian
Lie groups
control system
random matrix
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Confluence in Chip-Firing and Related Combinatorial Processes

Description:
Confluence is an important property in many combinatorial processes. A globally confluent process is one in which a fixed initial state always leads to a …
Year:
2022
Contributor:
Liscio, Patrick Hirsch (creator)
Klivans, Caroline (Advisor)
Guzman, Johnny (Reader)
Chan, Melody (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Combinatorics
Applied mathematics
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Data-Driven Mathematical Analysis with Applications in Dynamical Systems, Biology, and Social Justice

Description:
Abstract of Data-Driven Mathematical Analysis with Applications in Dynamical Systems, Biology, and Social Justice, by Rebecca Santorella Ph.D., Brown University, May 2022. As data becomes …
Year:
2022
Contributor:
Santorella, Rebecca (creator)
Sandstede, Bjorn (Advisor)
Singh, Ritambhara (Reader)
Harrison, Matthew (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Applied mathematics
dynamical systems
Computational biology
Fair Machine Learning
federal sentencing
data science
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Discontinuous Galerkin Methods for Wave Equations: the MLP Estimator for the TVB Constant in Limiters and Local DG Methods for a Carpet Cloak Model

Description:
This thesis contains two parts, including the development of a modified total variation bounded (TVB) limiter applied to the discontinuous Galerkin (DG) methods, and the …
Year:
2022
Contributor:
Yu, Xinyue (creator)
Shu, Chi-Wang (Advisor)
Guzman, Johnny (Reader)
Ainsworth, Mark (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Conservation laws (Mathematics)--Numerical solutions
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

High Order 2D Finite Element Methods with Extra Smoothness

Description:
Finite element methods (FEMs) are used to discretize partial differential equations in a wide array of applications, including fluid flow, solid mechanics, electromagnetism, optimal control, …
Year:
2022
Contributor:
Parker, Charles William (creator)
Ainsworth, Mark (Advisor)
Süli, Endre (Reader)
Karniadakis, George (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Numerical analysis
preconditioners
Finite element method
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Message Passing Dynamics of Belief Propagation Algorithms

Description:
Our work is motivated by the classical belief propagation algorithms which are well-known for obtaining state of the art results in certain settings, but often …
Year:
2022
Contributor:
Grim, Anna (creator)
Felzenszwalb, Pedro (Advisor)
Harrison, Matt (Reader)
Guzman, Johnny (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Inference
Approximation Algorithms
Graphical modeling (Statistics)
Belief Propagation
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Non-Markovian Interacting Particle Systems on Large Sparse Graphs: Hydrodynamic Limits and Marginal Characterizations

Description:
Consider a (possibly non-Markovian) interacting particle system (IPS) indexed by the nodes of a (possibly random) locally finite graph whose vertices and edges are equipped …
Year:
2022
Contributor:
Ganguly, Ankan (creator)
Ramanan, Kavita (Advisor)
Geman, Stuart (Reader)
Durrett, Rick (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Stochastic processes
Markov random fields
Hydrodynamic limit
local weak convergence
interacting particle systems
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Novel optimization algorithms for evaluating solution to certain high dimension (multi-time) Hamilton-Jacobi PDEs arising from optimal control

Description:
In this thesis, we study optimization algorithms for evaluating solutions to certain high dimension (multi-time) Hamilton-Jacobi Partial Differential equations arising from optimal control. There are …
Year:
2022
Contributor:
Kim, TaeWoo (creator)
Darbon, Jerome (Advisor)
Shu, Chi-Wang (Reader)
Guzman, Johnny (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Convex Optimization
optimal control
Hamilton-Jacobi equations
primal dual
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Overcoming the curse of dimensionality for solving high-dimensional Hamilton-Jacobi partial differential equations using neural networks and optimization algorithms

Description:
Hamilton-Jacobi PDEs and optimal control problems are widely used in many practical problems in control engineering, physics, financial mathematics, and machine learning. For instance, controlling …
Year:
2022
Contributor:
Meng, Tingwei (creator)
Darbon, Jerome (Advisor)
Karniadakis, George (Reader)
Shu, Chi-Wang (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Optimizations
Neural networks (Computer science)
optimal control
Hamilton-Jacobi equations
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Recent Advances in Splitting Methods Based on Robin-Robin Coupling Conditions

Description:
In this thesis we develop a loosely coupled splitting method for coupled problems called the Robin-Robin splitting method. As the name suggests, this method is …
Year:
2022
Contributor:
Durst, Rebecca Frances (creator)
Guzman, Johnny (Advisor)
Shu, Chi-Wang (Reader)
Burman, Erik (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Numerical analysis
Fluid-structure interaction--Mathematical models
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Sharp large deviation estimates and their applications to asymptotic convex geometry

Description:
The study of high-dimensional measures is an integral part of probability, statistics and asymptotic convex geometry, where the object of interest is the normalized volume …
Year:
2022
Contributor:
Liao, Yin-Ting (creator)
Ramanan, Kavita (Advisor)
Dupuis, Paul (Reader)
Paouris, Grigoris (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Convex geometry
Probabilities
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Variational and Bayesian Methods for Solving Hamilton–Jacobi Equations in Machine Learning and Imaging Science

Description:
The growing computational demands of data science applications pose a significant challenge to machine learning and the applied sciences. These applications have relied mainly on …
Year:
2022
Contributor:
Provencher Langlois, Gabriel (creator)
Darbon, Jerome (Advisor)
Dupuis, Paul (Reader)
Geman, Stuart (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Applied mathematics
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Items (1-13) out of 13 results