Xu, Jie

Email: xu924@purdue.edu

Office: MATH 439

Education

• 09/2010 -- 07/2015: Ph.D, supervised by Prof. Pingwen Zhang,
  School of Mathematical Science, Peking University.
• 09/2006 -- 07/2010: B.S.,
  School of Mathematical Science, Peking University.

Experiences

• 04/2016 -- now: Postdoc, Department of Mathematics, Purdue University. With Prof. Jie Shen.
• 08/2015 -- 03/2016: Visiting Scholar, School of Mathematical Science, Peking University.

Teaching

• Spring 2017, MA 266, Ordinary Differential Equations
• Spring 2018, MA 266, Ordinary Differential Equations
• Spring 2019, MA 266, Ordinary Differential Equations

Research Interest

• Modeling and simulation of liquid crystals
• Simulation of interface
• Numerical methods of gradient flows.

Publications

1. (With Pingwen Zhang) From microscopic theory to macroscopic theory: symmetries and order parameters of rigid molecules, Science China Mathematics, 57, 443-468(2014).
2. (With Chu Wang, An-Chang Shi and Pingwen Zhang) Computing Optimal Interfacial Structure of Modulated Phases, Communications in Computational Physics, 21, 1-15(2017).
3. (With Pingwen Zhang) The transmission of symmetry in liquid crystals, Communications in Mathematical Sciences, 15(1), 185-195(2017).
4. (With Fangfu Ye and Pingwen Zhang) A tensor model for nematic phases of bent-core molecules based on molecular theory, Multiscale Modeling and Simulation, 16(4), 1581-1602(2018).
5. (With Jie Shen and Pingwen Zhang) Approximating functions on SO(3) by Wigner D-matrix and applications, Journal of Scientific Computing, 74(3), 1706-1724(2018).
6. (With Pingwen Zhang) Calculating elastic constants of bent-core molecules from Onsager-theory-based tensor model, Liquid Crystals, 45(1), 22-31(2018).
7. (With Yixiang Luo and Pingwen Zhang) A Fast Algorithm for the Moments of Bingham Distribution, Journal of Scientific Computing, 75(3), 1337-1350(2018).
8. (With Pingwen Zhang) Onsager-theory-based dynamic model for nematic phases of bent-core molecules and star molecules, Journal of Non-Newtonian Fluid Mechanics, 251, 43-55(2018).
9. (With Jie Shen and Jiang Yang) The scalar auxiliary variable (SAV) approach for gradient flows, Journal of Computational Physics, 353, 407-416(2018).
10. (With Jie Shen) Stabilized predictor-corrector schemes for gradient flows with strong anisotropic free energy, Communications in Computational Physics, 24(3), 635-654(2018).
11. (With Jie Shen and Jiang Yang) A new class of efficient and robust energy stable schemes for gradient flows, in revision.
12. (With Jie Shen) Convergence and error analysis for the scalar auxiliary variable (SAV) schemes to gradient flows, SIAM Journal on Numerical Analysis, 56(5), 2895-2912(2018).

Package

• BinghamMoments: a fast routine for evaluating moments of Bingham distribution. Description and an example of application in liquid crystals.