seminars:anal
Differences
This shows you the differences between two versions of the page.
|
seminars:anal [2026/01/28 13:46] xxu |
seminars:anal [2026/02/22 12:09] (current) xxu |
||
|---|---|---|---|
| Line 64: | Line 64: | ||
| - | * **February 11th, Wednesday ** (4-5pm)\\ | + | |
| - | \\ **//Speaker //**: | + | * **Tuesday, February 10 (Joint with Data Science Seminar) ** (12:15-1:15pm)\\ |
| - | \\ **//Topic//**: | + | \\ **//Speaker //**: Dr. Yizeng Li (Department of Biomedical Engineering at Binghamton University) |
| + | \\ **//Topic//**: Multiphase Continuum Models for Cell Migration. | ||
| \\ \\ | \\ \\ | ||
| - | <WRAP box 80%> **//Abstract//**: | + | <WRAP box 80%> **//Abstract//**: Cell migration is a fundamental process in physiology and disease, yet it poses challenging problems in multiscale modeling and continuum mechanics. Cell motility arises from the coupling of intracellular transport, active force generation, and evolving geometry. Cytoskeletal dynamics, in particular actin turnover and force production, provides a rich setting for mathematical analysis. In this talk, I will present a mathematical framework for mammalian cell motility based on multiphase continuum models with moving boundaries. The formulation incorporates fluid-structure interaction and active stresses to describe the coupled evolution of cytoskeletal flow and cell shape. The model predicts how migration efficiency depends on actin dynamics and geometric features of the cell. If time permits, I will also present a mechanical-electrical-chemical coupled model for water-driven cell motility induced by polarized membrane ion transport. This second framework highlights how transport processes and force balance together generate directed motion. |
| + | |||
| + | Biography of the speaker: Yizeng Li is an Assistant Professor in the Department of Biomedical Engineering at Binghamton University. She received MS from Mathematics and PhD from the Department of Mechanical Engineering at the University of Michigan-Ann Arbor. Afterwards, she was a postdoctoral researcher at Johns Hopkins University's Department of Mechanical Engineering and Institute for NanoBioTechnology. Her backgrounds are in theoretical mechanics and applied mathematics with applications to biophysics and mechanobiology. Li develops physiology-based mathematical models for cell motility, polarization, volume regulation, electro-homeostasis, signal transduction, and other biophysics problems. She also combines mathematical models with experimental data to explain non-intuitive cell biology phenomena. | ||
| \\ | \\ | ||
| Line 74: | Line 77: | ||
| \\ \\ | \\ \\ | ||
| - | |||
| - | * **February 18th, Wednesday ** (4-5pm)\\ | ||
| - | \\ **//Speaker //**: | ||
| - | \\ **//Topic//**: | ||
| - | \\ \\ | ||
| - | <WRAP box 80%> **//Abstract//**: | ||
| - | |||
| - | \\ | ||
| - | </WRAP> | ||
| - | \\ \\ | ||
| Line 94: | Line 87: | ||
| \\ | \\ | ||
| </WRAP> | </WRAP> | ||
| - | \\ \\ | + | \\ |
| Line 106: | Line 98: | ||
| \\ | \\ | ||
| </WRAP> | </WRAP> | ||
| - | \\ \ | + | \\ |
| Line 119: | Line 111: | ||
| \\ \\ | \\ \\ | ||
| - | \ | + | |
| * **March 18th, Wednesday ** (4-5pm) \\ \\ | * **March 18th, Wednesday ** (4-5pm) \\ \\ | ||
| - | **//Speaker//**: \\ | + | **//Speaker//**: Zheng Sun (University of Alabama, Tuscaloosa)\\ |
| - | **//Topic//**: | + | **//Topic//**: On a numerical artifact of solving shallow water equations with a discontinuous bottom |
| \\ \\ | \\ \\ | ||
| - | <WRAP box 80%> **//Abstract//**: | + | <WRAP box 80%> **//Abstract//**: The nonlinear shallow water equations are used to model the free surface flow in rivers and coastal areas for which the horizontal length scale is much greater than the vertical length scale. They have wide applications in oceanic sciences and hydraulic engineering. In this talk, we study a numerical artifact of solving the shallow water equations over a discontinuous riverbed. For various first-order methods, we report that the numerical solution will form a spurious spike in the numerical momentum at the discontinuous point of the bottom. This artifact will cause the convergence to a wrong solution in many test cases. We present a convergence analysis to show that this numerical artifact is caused by the numerical viscosity imposed at the discontinuous point. Motivated by our analysis, we propose a numerical fix which works for the nontransonic problems. |
| Line 140: | Line 132: | ||
| **//Speaker//**: Yiming Zhao(Syracuse University) \\ | **//Speaker//**: Yiming Zhao(Syracuse University) \\ | ||
| **//Topic//**: TBD | **//Topic//**: TBD | ||
| - | |||
| - | |||
| - | |||
| - | |||
| - | |||
| - | |||
| \\ \\ | \\ \\ | ||
| <WRAP box 80%> **//Abstract//**: | <WRAP box 80%> **//Abstract//**: | ||
| Line 161: | Line 147: | ||
| + | \\ | ||
| </WRAP> | </WRAP> | ||
| \\ \\ | \\ \\ | ||
| Line 170: | Line 156: | ||
| **//Speaker//**: \\ | **//Speaker//**: \\ | ||
| **//Topic//**: | **//Topic//**: | ||
| - | |||
| \\ \\ | \\ \\ | ||
| <WRAP box 80%> **//Abstract//**: | <WRAP box 80%> **//Abstract//**: | ||
| Line 181: | Line 166: | ||
| - | * **April 15th, Wednesday, 4:00-5:00pm \\ \\ | + | * **April 15th, Wednesday,** 4:00-5:00pm \\ \\ |
| - | **//Speaker//**: \\ | + | **//Speaker//**: Brian Kirby(Binghamton University) \\ |
| - | **//Topic//**: | + | **//Topic//**: PhD Thesis Defense |
| \\ \\ | \\ \\ | ||
| <WRAP box 80%> **//Abstract//**: | <WRAP box 80%> **//Abstract//**: | ||
| Line 191: | Line 176: | ||
| \\ \\ | \\ \\ | ||
| - | * **April 22th, Wednesday ** (4-5pm) ****\\ \\ | + | * **April 22th, Wednesday ** (4-5pm) \\ \\ |
| **//Speaker//**: \\ | **//Speaker//**: \\ | ||
| **//Topic//**: | **//Topic//**: | ||
| Line 208: | Line 193: | ||
| - | * **April 29th, Wednesday ** (4-5pm) \\ \\ | + | **April 29th, Wednesday ** (4-5pm) \\ \\ |
| - | **//Speaker//**: \\ | + | **//Speaker//**: Yahong Yang (Georgia Institute of Technology) \\ |
| - | **//Topic//**: | + | **//Topic//**: Multiscale Neural Networks for Approximating Green’s Functions and Operators |
| \\ \\ | \\ \\ | ||
| - | <WRAP box 80%> **//Abstract//**: | + | <WRAP box 80%> **//Abstract//**: Neural networks (NNs) have been widely used to solve partial differential equations (PDEs) with broad applications in physics, biology, and engineering. One effective approach for solving PDEs with a fixed differential operator is to learn the associated Green’s function. However, Green’s functions are notoriously difficult to approximate due to their poor regularity, often requiring large neural networks and long training times. |
| + | |||
| + | In this talk, we address these challenges by leveraging multiscale neural networks to learn Green’s functions efficiently. Through theoretical analysis based on multiscale Barron space techniques, together with numerical experiments, we show that the multiscale approach significantly reduces the required network size and accelerates training. We then extend this framework to operator learning, enabling neural networks to efficiently and accurately learn the mapping from coefficient functions to Green’s functions. | ||
| Line 223: | Line 210: | ||
| * **May 6th, Wednesday ** (4-5pm) \\ \\ | * **May 6th, Wednesday ** (4-5pm) \\ \\ | ||
| - | **//Speaker//**: \\ | + | **//Speaker//**: \\ |
| - | **//Topic//**: | + | **//Topic//**: |
| \\ \\ | \\ \\ | ||
seminars/anal.1769626014.txt · Last modified: 2026/01/28 13:46 by xxu