Changhui Tan
I am a postdoctoral research associate in CSCAMM and Department of Mathematics, University of Maryland.
Mathematical and numerical analysis to variable-order mobile-immobile time-fractional diffusion equations
Speaker: Xiangcheng Zheng (University of South Carolina)
We proved the wellposedness of variable-order mobile-immobile time-fractional diffusion equations and the regularity of their solutions. Optimal-order finite element approximation was presented and analyzed. Numerical experiments were carried out for demonstration.
Time: January 31, 2020 2:30pm-3:30pm
Location: LC317R
Lagrangian Front Tracking and Applications to Conservation Law, Fluid Mixing, and Phase Transition Problems
Speaker: Xiaolin Li (Stony Brook University)
In this talk, I will review the history of the Lagrangian front tracking method and the computational platform built on this methodology. I will review the front tracking in the study of fluid interface instabilities, including Rayleigh-Taylor instability, Richtmyer Meshkov instability and fluid mixing induced by these instabilities. I will also introduce a fully conservative front tracking scheme and its application in the phase transition problem.
Time: March 20, 2020 2:30pm-3:30pm
Location: LC317R
Host: Xinfeng Liu
Traveling Wave of Gray-Scott System: Results and Perspective
Speaker: Yuanwei Qi (University of Central Florida)
In this talk, I shall report some recent progress on the existence and multiplicity of traveling waves to one of the most important models in Turing Pattern Formation. In addition, I shall pose some questions which are wide open which demand new ideas and fresh approaches. This is a joint-work with Xinfu Chen et al.
Time: January 17, 2020 2:30pm-3:30pm
Location: LC317R
Host: Changhui Tan
ACM Seminar Schedule
Regular seminar talk time and location: Fridays 2:30pm-3:30pm @ LeConte 440.
2024 and After
Please see HERE for the schedule.
Fall 2023
Spring 2023
Fall 2022
September 30 | Zhilin Li (North Carolina State University) | Host: Qi Wang |
(Postponed to October 7) | Title: An Overview of Augmented Strategy and Applications [Virtual] | |
October 21 | Jianliang Qian (Michigan State University) | Host: Lili Ju |
Title: Hadamard-Babich Ansatz for Point-source Maxwell's Equations [Virtual] | ||
October 28 | Federico Pasqualotto (Duke University) | Host: Siming He |
LeConte 205 | Title: On the Construction of 3D Incompressible Euler Equilibria by Magnetic Relaxation [In Person] | |
November 11 | Amir Sagiv (Columbia University) | Host: Wolfgang Dahmen |
Title: A Measure Perspective on Uncertainty Quantification [Virtual] | ||
November 18 | Jing An (Duke University) | Host: Siming He |
LeConte 205 | Title: Quantitative Steepness, Semi-FKPP Reactions, and Pushmi-pullyu Fronts [In Person] | |
December 2 | Pierre-Emmanuel Jabin (Pennsylvania State University) | Host: Changhui Tan |
Title: A New Approach to the Mean-field Limit of Vlasov-Fokker-Planck Equations [Virtual] |
Spring 2022
February 18 | Jiahong Wu (Oklahoma State University) | Host: Changhui Tan |
Title: Stabilizing Phenomenon for Incompressible Fluids | ||
March 4 | Ming Chen (University of Pittsburgh) | Host: Changhui Tan |
Title: Orbital Stability for Internal Waves | ||
March 11 | Spring Break | |
March 18 | SIAM Conference on Analysis of Partial Differential Equations | |
March 25 | Qingtian Zhang (West Virginia University) | Host: Changhui Tan |
Title: Global Solutions of Quasi-geostrophic Shallow Water Front Problems | ||
April 8 | Joint Math Meeting | |
April 15 | Guowei Wei (Michigan State University) | Host: Qi Wang |
Title: How Math and AI are Revolutionizing Biosciences | ||
April 22 | Ziad Musslimani (Florida State University) | Host: Qi Wang |
Title: Spectral Renormalizations Methods in Physics |
Fall 2021
Spring 2021
Fall 2020
Spring 2020
January 17 | Yuanwei Qi (University of Central Florida) | Host: Changhui Tan |
Title: Traveling Wave of Gray-Scott System: Results and Perspective | ||
January 31 | Xiangcheng Zheng (University of South Carolina) | Math Graduate Student |
Title: Mathematical and numerical analysis to variable-order mobile-immobile time-fractional diffusion equations | ||
February 21 | Hailiang Liu (Iowa State University) | Host: Changhui Tan |
Title: Efficient, positive, and energy stable schemes for Poisson-Nernst-Planck systems | ||
March 20 | Xiaolin Li (Stony Brook University) | Host: Xinfeng Liu |
(Cancelled) | Title: Lagrangian Front Tracking and Applications to Conservation Law, Fluid Mixing, and Phase Transition Problems | |
March 27 | Rihui Lan (University of Nevada, Las Vegas) | Host: Lili Ju |
(Postponed) | Title: The Monolithic Arbitrary Lagrangian-Eulerian (ALE) Finite Element Analysis of Moving Interface Problems |
2019 and before
The schedule can be found HERE and HERE.
MacOS change keychain password
In the MacOS system, the keychain password has to match the user password in order to use keychain appropriately. In my case, they have to match in order to allow Apple Watch to unlock the Mac.
The official way to change the keychain password can be found HERE. However, in my case, the "Change password for keychain login" option is in gray and can not be selected. One solution is the following:
Open terminal and type in
security set-keychain-password
Then, type in old password and then new password. The password is then changed. This does not require admin access.
A sharp critical threshold for a traffic flow model with look-ahead dynamics
Yongki Lee, and Changhui Tan
Communications in Mathematical Sciences, Volume 20, No. 4, pp. 1151-1172 (2022).
Abstract
We study a Lighthill-Whitham-Richards (LWR) type traffic flow model, with a nonlocal look-ahead interaction that has a slow-down effect depending on the traffic ahead. We show a sharp critical threshold condition on the initial data that distinguishes global smooth solutions and finite- time wave breakdown. It is well-known that the LWR model leads to a finite-time shock formation, representing the creation of traffic jams, for generic smooth initial data with finite mass. Our result shows that the nonlocal slowdown effect can help to prevent shock formations, for a class of subcritical initial data.
doi:10.4310/CMS.2022.v20.n4.a9 | |
Download the Published Version | |
This work is supported by NSF grants DMS #1853001 and DMS #2108264 | |
This work is supported by a UofSC VPR ASPIRE I grant |
On the Euler-alignment system with weakly singular communication weights
Changhui Tan
Nonlinearity, Volume 33, No 4, pp. 1907-1924 (2020).
Abstract
We study the pressureless Euler equations with nonlocal alignment interactions, which arises as a macroscopic representation of the Cucker–Smale model on animal flocks. For the Euler-alignment system with bounded interactions, a critical threshold phenomenon is proved in Tadmor and Tan (2014 Phil. Trans. R. Soc. A 372 20130401), where global regularity depends on initial data. With strongly singular interactions, global regularity is obtained in Do et al (2018 Arch. Ration. Mech. Anal. 228 1–37), for all initial data. We consider the remaining case when the interaction is weakly singular. We show a critical threshold, similar to the system with bounded interaction. However, different global behaviors may happen for critical initial data, which reveals the unique structure of the weakly singular alignment operator.
doi:10.1088/1361-6544/ab6c39 | |
Download the Published Version | |
This work is supported by NSF grant DMS #1853001 |
Honors and Awards
2013-2014 | Ann G. Wylie Dissertation Fellowship |
SIAM Student Travel Award | |
AMS Graduate Student Travel Grant | |
Kaplan Travel Grant | |
2011-2012 | Mark E. Lachtman Graduate Student Award |
Jacob K. Goldhaber Travel Award | |
2010-2011 | Kaplan Travel Grant |
2008-2010 | Graduate Fellowship in University of Maryland |
2007-2008 | First Honor Graduates in Beijing |
"Outstanding University Graduates" in Peking University | |
2006-2007 | Triple-Good Student in Peking University |
Chinese Economical Research Scholarship | |
2005-2006 | Triple-Good Student in Peking University |
Baogang Scholarship | |
2004-2005 | Triple-Good Student in Peking University |
Guanghua Scholarship |
Conference, Workshops and Seminars
2023
2023.6.2 | The 13th AIMS Conference on Dynamical Systems, Differential Equations and Applications, University of North Carolina, Wilmington. |
Talk: Collective behaviors in macroscopic swarming dynamics. | |
2023.3.19 | AMS Sectional Meeting, Special Session on Qualitative Aspects of Nonlinear PDEs: Well-posedness and Asymptotics, Georgia . |
Talk: The flow of polynomial roots under differentiation. | |
2023.2.17 | RTG Seminar, University of South Carolina. |
Talk: Nonlocal traffic flow models. |
2022
2021
2021.10.8 | PIMS-SFU Computational Math Seminar, Simon Fraser University. |
Talk: The flow of polynomial roots under differentiation. | |
2021.5.4 | PDE/Analysis Seminar, BICRM, Peking University. |
Talk: Eulerian dynamics in multi-dimensions with radial symmetry. | |
2021.4.19 | Analysis and Applied Mathematics Seminar, University of Illinois Chicago. |
Talk: The flow of polynomial roots under differentiation. | |
2021.3.30 | Applied Math & Analysis Seminar, Duke University. |
Talk: Nonlocal traffic flow models and the prevention of traffic jams. | |
2021.3.26 | Zu Chongzhi Colloquium, Duke Kunshan University. |
Talk: The flow of polynomial roots under differentiation. |
2020
2020.11.19 | INS Seminar, Shanghai Jiao Tong University. |
Talk: Nonlocal traffic flow models and the prevention of traffic jams. | |
2020.10.28 | Mathematics Colloquium, Old Dominion University. |
Talk: Self-organized dynamics: aggregation and flocking. | |
2020.9.28 | CAM Seminar, Iowa State University. |
Talk: Nonlocal traffic flow models. |
2019
2018
2017
Singularity formation for a fluid mechanics model with nonlocal velocity
Changhui Tan
Communications in Mathematical Sciences, Volume 17, No 7, pp. 1779-1794 (2019).
Abstract
We study a 1D fluid mechanics model with nonlocal velocity. The equation can be viewed as a fractional porous medium flow, a 1D model of quasi-geostrophic equation, and also a special case of the Euler alignment system. For strictly positive smooth initial data, global regularity has been proved in [Do, Kiselev, Ryzhik and Tan, Arch. Ration. Mech. Anal., 228(1):1–37, 2018]. We construct a family of non-negative smooth initial data so that solution is not \(C^1\)-uniformly bounded. Our result indicates that strict positivity is a critical condition to ensure global regularity of the system. We also extend our construction to the corresponding models in multi-dimensions.
doi:10.4310/CMS.2019.v17.n7.a2 | |
Download the Published Version | |
This work is supported by NSF grant DMS #1853001 |