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math.NA2022
Phase field modeling and computation of vesicle growth or shrinkage
Xiaoxia Tang, Shuwang Li, John S. Lowengrub +1
We present a phase field model for vesicle growth or shrinkage induced by an osmotic pressure due to a chemical potential gradient. The model consists of an Allen-Cahn equation des…
math.NA2019
Complex Far-Field Geometries Determine the Stability of Solid Tumor Growth with Chemotaxis
Min-Jhe Lu, Chun Liu, John Lowengrub +1
In this paper, we develop a sharp interface tumor growth model to study the effect of the tumor microenvironment using a complex far-field geometry that mimics a heterogeneous dist…
math.NA2018
Higher-order accurate diffuse-domain methods for partial differential equations with Dirichlet boundary conditions in complex, evolving geometries
Fei Yu, Zhenlin Guo, John Lowengrub
The diffuse-domain, or smoothed boundary, method is an attractive approach for solving partial differential equations in complex geometries because of its simplicity and flexibilit…