学术论文集(英文)
Changhui Tan

Changhui Tan

I am a postdoctoral research associate in CSCAMM and Department of Mathematics, University of Maryland. 

 

Thomas Hamori and Changhui Tan


Abstract

We present a new family of second-order traffic flow models, extending the Aw-Rascle-Zhang (ARZ) model to incorporate nonlocal interactions. Our model includes a specific nonlocal Arrhenius-type look-ahead slowdown factor. We establish both local and global well-posedness theories for these nonlocal ARZ models.
In contrast to the local ARZ model, where generic smooth initial data typically lead to finite-time shock formation, we show that our nonlocal ARZ model exhibits global regularity for a class of smooth subcritical initial data. Our result highlights the potential of nonlocal interactions to mitigate shock formations in second-order traffic flow models.
Our analytical approach relies on investigating phase plane dynamics. We introduce a novel comparison principle based on a mediant inequality to effectively handle the nonlocal information inherent in our model.


 This work is supported by NSF grants DMS #2108264 and DMS #2238219
星期四, 07 3月 2024 15:58

Nonlocal Models: Analysis and Applications

Confirmed Speakers

  • Amimikh Biswas, University of Maryland, Baltimore County.
  • Alina Chertock, North Carolina State University.
  • Ronald DeVore, Texas A&M University.
  • Ming Chen, University of Pittsburgh.
  • Gautam Iyer, Carnegie Mellon University.
  • Pierre-Emmanuel Jabin, Pennsylvania State University.
  • Qin Li, University of Wisconsin, Madison.
  • Hailiang Liu, Iowa State University.
  • Jian-Guo Liu, Duke University.
  • Mauro Maggioni, Johns Hopkins University.
  • Anna Mazuccato, Pennsylvania State University.
  • Sebastien Motsch, Arizona State University.
  • Ronghua Pan, Georgia Institute of Technology.
  • Keith Promislow, Michigan State University.
  • Roman Shvydkoy, University of Illinois, Chicago.
  • Weiran Sun, Simon Fraser University.
  • Li Wang, University of Minnesota. 

Registration

  • Register by May 10th HERE .
  • A limited amount of travel and local lodging is available for researchers in the early stages of their careers who want to attend the full program, especially for graduate students and post-doctoral fellows.

Travel and Hotel Information

  • Information will be updated in late March.

Organizing Committee

  • Changhui Tan, University of South Carolina. Email: 该Email地址已收到反垃圾邮件插件保护。要显示它您需要在浏览器中启用JavaScript。
  • Siming He, University of South Carolina.
  • Ming Zhong, Illinois Institute of Technology.

Acknowledgement

 

Xiang Bai, Changhui Tan and Liutang Xue


Abstract

We study the Cauchy problem of the compressible Euler system with strongly singular velocity alignment. We establish a global well-posedness theory for the system with small smooth initial data. Additionally, we derive asymptotic emergent behaviors for the system, providing time decay estimates with optimal decay rates. Notably, the optimal decay rate we obtain does not align with the corresponding fractional heat equation within our considered range, where the parameter \(\alpha\in(0,1)\). This highlights the distinct feature of the alignment operator.


 This work is supported by NSF grants DMS #2108264 and DMS #2238219

 

McKenzie Black, and Changhui Tan


Abstract

We investigate a class of Vlasov-type kinetic flocking models featuring nonlinear velocity alignment. Our primary objective is to rigorously derive the hydrodynamic limit leading to the compressible Euler system with nonlinear alignment. This study builds upon the work by Figalli and Kang [Anal. PDE, 12(3), 843-866, 2018], which addressed the scenario of linear velocity alignment using the relative entropy method. The introduction of nonlinearity gives rise to an additional discrepancy in the alignment term during the limiting process. To effectively handle this discrepancy, we employ the monokinetic ansatz in conjunction with the relative entropy approach. Furthermore, our analysis reveals distinct nonlinear alignment behaviors between the kinetic and hydrodynamic systems, particularly evident in the isothermal regime.


 This work is supported by NSF grants DMS #2108264 and DMS #2238219

 Speaker: Yuan-Nan Young (New Jersey Institute of Technology)

The Stoichiometric Model for the interaction of centrosomes with cortically anchored pulling motors, through their associated microtubules (MTs), has been applied to study key steps in the cell division such as spindle positioning and elongation. In this work we extend the original Stoichiometric Model to incorporate (1) overlap in the cortical motors, and (2) the dependence of velocity in the detachment rate of MTs from the cortical motors. We examine the effects of motor overlap and velocity-dependent detachment rate on the centrosome dynamics, such as the radial oscillation around the geometric center of the cell, the nonlinear nature (supercritical and subcritical Hopf bifurcation) of such oscillation, and the nonlinear orbital motions previously found for a centrosome. We explore biologically feasible parameter regimes where these effects may lead to significantly different centrosome/nucleus dynamics. Furthermore we use this extended Stoichiometric Model to study the migration of a nucleus being positioned by a centrosome. This is joint work with Justin Maramuthal, Reza Farhadifar and Michael Shelley.
 

Time: December 8, 2023 2:30pm-3:30pm
Location: Virtually via Zoom
Host: Paula Vasquez

 Speaker: Quyuan Lin (Clemson University)

Large scale dynamics of the ocean and the atmosphere are governed by the primitive equations (PE). In this presentation, I will first review the derivation of the PE and some well-known results for this model, including well-posedness of the viscous PE and ill-posedness of the inviscid PE. The focus will then shift to discussing singularity formation and the stability of singularities for the inviscid PE, as well as the effect of fast rotation (Coriolis force) on the lifespan of the analytic solutions. Finally, I will talk about a machine learning algorithm, the physics-informed neural networks (PINNs), for solving the viscous PE, and its rigorous error estimate.
 

Time: November 17, 2023 2:30pm-3:30pm
Location: LeConte 440
Host: Changhui Tan

 Speaker: Adrian Tudorascu (West Virginia University)

We study Zeldovich's Sticky-Particles system when the evolution is confined to arbitrary closed subsets of the real line. Only the sticky boundary condition leads to a rigorous formulation of the initial value problem, whose well-posedness is proved under the Oleinik and initial strong continuity of energy conditions. For solutions confined to compact sets a long-time asymptotic limit is shown to exist.
 

Time: October 27, 2023 2:30pm-3:30pm
Location: LeConte 440
Host: Changhui Tan

 Speaker: Yuehaw Khoo (University of Chicago)

Tensor-network ansatz has long been employed to solve the high-dimensional Schrödinger equation, demonstrating linear complexity scaling with respect to dimensionality. Recently, this ansatz has found applications in various machine learning scenarios, including supervised learning and generative modeling, where the data originates from a random process. In this talk, we present a new perspective on randomized linear algebra, showcasing its usage in estimating a density as a tensor-network from i.i.d. samples of a distribution, without the curse of dimensionality, and without the use of optimization techniques. Moreover, we illustrate how this concept can combine the strengths of particle and tensor-network methods for solving high-dimensional PDEs, resulting in enhanced flexibility for both approaches.
 

Time: December 1, 2023 3:40pm-4:40pm
Location: LeConte 440
Host: Wuchen Li

星期三, 18 10月 2023 16:04

Hybrid quantum classical algorithms

 Speaker: Xiantao Li (Pennsylvania State University)

Quantum computing has recently emerged as a potential tool for large-scale scientific computing. In sharp contrast to their classical counterparts, quantum computers use qubits that can exist in superposition, potentially offering exponential speedup for many computational problems. Current quantum devices are noisy and error-prone, and in near term, a hybrid approach is more appropriate. I will discuss this hybrid framework using three examples: quantum machine learning, quantum algorithms for density-functional theory and quantum optimal control. In particular, this talk will outline how quantum algorithms can be interfaced with a classical method, the convergence properties and the overall complexity.
 

Time: November 3, 2023 2:30pm-3:30pm
Location: LeConte 440
Host: Yi Sun

 Speaker: Jiajia Yu (Duke University)

Mean-field games study the Nash Equilibrium in a non-cooperative game with infinitely many agents. Most existing works study solving the Nash Equilibrium with given cost functions. However, it is not always straightforward to obtain these cost functions. On the contrary, it is often possible to observe the Nash Equilibrium in real-world scenarios. In this talk, I will discuss a bilevel optimization approach for solving inverse mean-field game problems, i.e., identifying the cost functions that drive the observed Nash Equilibrium. With the bilevel formulation, we retain the essential characteristics of convex objective and linear constraint in the forward problem. This formulation permits us to solve the problem using a gradient-based optimization algorithm with a nice convergence guarantee. We focus on inverse mean-field games with unknown obstacles and unknown metrics and establish the numerical stability of these two inverse problems. In addition, we prove and numerically verify the unique identifiability for the inverse problem with unknown obstacles. This is a joint work with Quan Xiao (RPI), Rongjie Lai (Purdue) and Tianyi Chen (RPI).
 

Time: October 6, 2023 3:40pm-4:40pm
Location: LeConte 440
Host: Wuchen Li

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