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Author:

Zheng, Bin

Title:

Finite Element Approximations of High Order Partial Differential Equations

Graduate Program:

Mathematics

Keywords:

finite element methods
high order partial differential equations
magnetohydrodynamics

File:

Download mythesis.pdf

Committee Members:

Jinchao Xu, Committee Chair/Co-Chair
Chun Liu, Committee Member
Eric M Mockensturm, Committee Member
Victor Nistor, Committee Member
Ludmil Tomov Zikatanov, Committee Member

Author:

Xue, Guangri

Title:

Numerical Methods for Multiphysics, Multiphase, and Multicomponent Models for Fuel Cells

Graduate Program:

Mathematics

Keywords:

Numerical methods
multiphysics
multicomponent
fuel cell
multiphase
coupling

File:

Download thesis-GuangriXue.pdf

Committee Members:

Jinchao Xu, Committee Chair/Co-Chair
Ludmil Tomov Zikatanov, Committee Member
Chun Liu, Committee Member
Alberto Bressan, Committee Member
Chao Yang Wang, Committee Member

Author:

Sun, Huan

Title:

AN ENERGETIC VARIATIONAL APPROACH TO MODELING COMPLEX FLUIDS AND ITS NUMERICAL SIMULATIONS

Graduate Program:

Mathematics

Keywords:

PDE
variational techniques
complex fluids
numerical simulations

File:

Download thesis_main.pdf

Committee Members:

Chun Liu And James Brannick, Dissertation Advisor/Co-Advisor
Chun Liu, Committee Chair/Co-Chair
James Joseph Brannick, Committee Chair/Co-Chair
Xiantao Li, Committee Member
Yuxi Zheng, Committee Member
Ludmil Tomov Zikatanov, Committee Member
Ralph H Colby, Committee Member

Author:

Wang, Jiakou

Title:

STOCHASTIC AND DETERMINISTIC COAGULATION MODELS, THEIR NUMERICAL APPROXIMATIONS AND APPLICATIONS TO CELL AGGREGATION

Graduate Program:

Mathematics

Keywords:

cell aggregation
coagulation equation
stochastic model
time relaxed method

File:

Download Wang-Dissertation.pdf

Committee Members:

Qiang Du, Committee Chair/Co-Chair
Cheng Dong, Committee Member
Chun Liu, Committee Member
Suzanne Michelle Shontz, Committee Member
Ludmil Tomov Zikatanov, Committee Member

Author:

Chen, Long

Title:

Robust and Accurate Algorithms for Solving Anisotropic Singularities

Graduate Program:

Mathematics

Keywords:

mesh adaptation
anisotropic error estimate
convection dominated problem
singularly perturbed problem
optimal Delaunay triangulation
nonlinear approximation

File:

Download MyThesis.pdf

Committee Members:

Jinchao Xu, Committee Chair/Co-Chair
Qiang Du, Committee Member
Chun Liu, Committee Member
James Z Wang, Committee Member
Ludmil Tomov Zikatanov, Committee Member

Author:

Zhang, Lei

Title:

Phase field model for the nucleation in solid state phase transformations: Theories, Algorithms and Applications

Graduate Program:

Mathematics

Keywords:

Phase field
nucleation
critical nucleus
solid state

File:

Download Lei-Dissertation.pdf

Committee Members:

Qiang Du, Dissertation Advisor/Co-Advisor
Qiang Du, Committee Chair/Co-Chair
Long Qing Chen, Committee Member
Chun Liu, Committee Member
Ludmil Tomov Zikatanov, Committee Member
Xiantao Li, Committee Member

Author:

Li, Manlin

Title:

ANALYSIS OF DETERMINISTIC AND STOCHASTIC IMPLICIT INTERFACE MODELS OF FLUID-INTERFACE INTERACTIONS

Graduate Program:

Mathematics

Keywords:

SIIM
phase field
implict interface

File:

Download Thesis-ManlinLi.pdf

Committee Members:

Qiang Du, Dissertation Advisor/Co-Advisor
Qiang Du, Committee Chair/Co-Chair
Chun Liu, Committee Member
Ludmil Tomov Zikatanov, Committee Member
Xiantao Li, Committee Member
John Fricks, Committee Member

Author:

Ryham, Rolf Josef

Title:

An Energetic Variational Approach to Mathematical Modeling of Charged Fluids: Charge Phases, Simulation and Well Posedness

Graduate Program:

Mathematics

Keywords:

ER fluid
electrokinetics
Nernst-Plank-Poisson
phase field

File:

Download RolfRyhamThesis.pdf

Committee Members:

Chun Liu, Committee Chair/Co-Chair
Ludmil Tomov Zikatanov, Committee Chair/Co-Chair
Qiang Du, Committee Member
Yousry Azmy, Committee Member
Fanghua Lin, Committee Member

Author:

Wang, Xiaoqiang

Title:

PHASE FIELD MODELS AND SIMULATIONS OF VESICLE BIO-MEMBRANES

Graduate Program:

Mathematics

Keywords:

Vesicle membrane
elastic bending energy
energetic variational approach
diffusive interface approximation
phase field model
numerical methods
three dimensional simulation
Navier-Stokes equation

File:

Download bubble.pdf

Committee Members:

Qiang Du, Committee Chair/Co-Chair
Chun Liu, Committee Member
Ludmil Tomov Zikatanov, Committee Member
Hongyuan Zha, Committee Member

Author:

Xu, Xiang

Title:

Topics on Stability of Complex Fluid Models

Graduate Program:

Mathematics

Keywords:

stability analysis
energetic variational approaches
long time behavior
Parodi's relation

File:

Download Xiang_Xu-Dissertation.pdf

Committee Members:

Chun Liu, Dissertation Advisor/Co-Advisor
Chun Liu, Committee Chair/Co-Chair
Ludmil Tomov Zikatanov, Committee Member
Andrew Leonard Belmonte, Committee Member
Francesco Costanzo, Committee Member