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Research

Here are the latest updates for Changhui Tan's research profile.

Here is the Curriculum Vitae and List of Publications.

Thursday, 17 April 2014 16:01

Ph.D. Defense

 

I have finished my Ph.D. defense today.


Committees

Prof. Eitan Tadmor (Chair/Advisor), Prof. Pierre-Emmanuel Jabin, Prof. Dave Levermore, Prof. Antoine Mellet and Prof. Howard Elman (Dean's representative).


My thesis title is Multi-scale problems on collective dynamics and image processing.

   doi:10.13016/M2WG6T
 Download the Ph.D. Thesis

 

Eitan Tadmor, and Changhui Tan

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372.2028 (2014): 20130401.


Abstract

We study the large-time behavior of Eulerian systems augmented with non-local alignment. Such systems arise as hydrodynamic descriptions of agent-based models for self-organized dynamics, e.g. Cucker & Smale (2007 IEEE Trans. Autom. Control 52, 852–862. (doi:10.1109/TAC.2007.895842)) and Motsch & Tadmor (2011 J. Stat. Phys. 144, 923–947. (doi:10.1007/s10955-011-0285-9)) models. We prove that, in analogy with the agent-based models, the presence of non-local alignment enforces strong solutions to self-organize into a macroscopic flock. This then raises the question of existence of such strong solutions. We address this question in one- and two-dimensional set-ups, proving global regularity for subcritical initial data. Indeed, we show that there exist critical thresholds in the phase space of the initial configuration which dictate the global regularity versus a finite-time blow-up. In particular, we explore the regularity of non-local alignment in the presence of vacuum.


   doi:10.1098/rsta.2013.0401
  Download the Published Version

 

Eitan Tadmor, and Changhui Tan

"Nonlinear Partial Differential Equations", Proceedings of the 2010 Abel Symposium held in Oslo, Sep. 2010 (H. Holden & K. Karlsen eds.), Abel Symposia 7, Springer 2011, 255-269.


Abstract

We implement the hierarchical decomposition introduced in [Ta15], to construct uniformly bounded solutions of the problem \(\nabla\cdot U = F\), where the two-dimensional data is in the critical regularity space, \(F\in L^2_{\#}(\mathbb{T}^2)\). Criticality in this context, manifests itself by the lack of linear mapping, \(F\in L^2_{\#}(\mathbb{T}^2)\to U\in L^{\infty}(\mathbb{T}^2,\mathbb{R}^2)\) [BB03]. Thus, the intriguing aspect here is that although the problem is linear, the construction of its uniformly bounded solutions is not.


   doi:10.1007/978-3-642-25361-4_14
  Download the Published Version

 

Yan-jun Guo, Mao Pan, Fei Yan, Zhe Wang, Changhui Tan, and Tiao Lu

Journal of PLA University of Science and Technology (Natural Science Edition), Volume 26, No 1, pp. 185-206 (2016).


Abstract

To enhance the accuracy of three-dimensional geological model, emphasize the high local relevance characteristics of the complex geological bodies, and avoid complicated calculation and dependence on human experience in traditional interpolation methods, the natural neighbor interpolation (NNI) method was used for three-dimensional discrete data interpolation in the process of modeling. But the existing NNI method could not be applied to the boundary interpolation of finite fields, which was the most difficult problem of its application in three-dimensional geological modeling. Based on the geometry of Voronoi Cells and Delaunay Triangles, the shape function was constructed using non-Sibsonian (Laplace) interpolation method. The continuity of the boundary in NNI method was proven, the boundary interpolation was implemented and the computational complexity was reduced. The accuracy and validity of the method were proven by building the city geological model.


   doi:10.3969/j.issn.1009-3443.2009.06.026
  Download the Published Version

The paper is related to the undergraduate thesis: Numerical analysis and algorithm design in natural neighbor method.

  Download the Undergraduate Thesis (In Chinese)
Sunday, 31 August 2008 00:26

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
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