49 citations · 56 across the 7 of their papers we have counts for
8 papers
Pattern formation in a Reaction-Diffusion Model for Amyloid- and Tau Interactions in Alzheimer's Disease
Sun Lee, Wenrui Hao
Alzheimer's disease (AD) is characterized by the accumulation of Amyloid- () plaques and hyperphosphorylated Tau proteins. However, many individuals exhibit substantial …
Numerical Identification of Stationary States and Their Stability in a Model of Quantum Droplets
Sun Lee, Panayotis G. Kevrekidis, Wenrui Hao
In this work, we are motivated by a recent variant of the nonlinear Schrodinger (NLS) equation describing cold, dilute atomic condensates with quantum fluctuation effects. Our goal…
Energy Approach from -Graph to Continuum Diffusion Model with Connectivity Functional
Yahong Yang, Sun Lee, Jeff Calder +1
We derive an energy-based continuum limit for -graphs endowed with a general connectivity functional. We prove that the discrete energy and its continuum counterpart d…
Optimal Control For Anti-Abeta Treatment in Alzheimer's Disease using a Reaction-Diffusion Model
Sun Lee, Chiu-Yen Kao, Zhiyuan Li +3
Alzheimer's disease (AD) is a progressive neurodegenerative disorder that severely impairs survival and quality of life. While anti-amyloid beta (Abeta) therapies can slow disease…
An Efficient Quasi-Newton Method with Tensor Product Implementation for Solving Quasi-Linear Elliptic Equations and Systems
Wenrui Hao, Sun Lee, Xiangxiong Zhang
In this paper, we introduce a quasi-Newton method optimized for efficiently solving quasi-linear elliptic equations and systems, with a specific focus on GPU-based computation. By…
Stability and Robustness of Time-discretization Schemes for the Allen-Cahn Equation via Bifurcation and Perturbation Analysis
Wenrui Hao, Sun Lee, Xiaofeng Xu +1
The Allen-Cahn equation is a fundamental model for phase transitions, offering critical insights into the dynamics of interface evolution in various physical systems. This paper in…
Companion-Based Multi-Level Finite Element Method for Computing Multiple Solutions of Nonlinear Differential Equations
Wenrui Hao, Sun Lee, Young Ju Lee
The use of nonlinear PDEs has led to significant advancements in various fields, such as physics, biology, ecology, and quantum mechanics. However, finding multiple solutions for n…
A Brief Technical History of the Large-Area Picosecond Photodetector (LAPPD) Collaboration
Bernhard W. Adams, Klaus Attenkofer, Mircea Bogdan +38
The Large Area Picosecond PhotoDetector (LAPPD) Collaboration was formed in 2009 to develop large-area photodetectors capable of time resolutions measured in pico-seconds, with acc…