徐劼 Xu, Jie

Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences.

Email: xujie AT lsec.cc.ac.cn

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

• 09/2019 -- current: Assistant Professor/Associate Professor, ICMSEC, AMSS, CAS.
• 04/2016 -- 08/2019: Visiting Assistant Professor/Postdoc, Department of Mathematics, Purdue University. With Prof. Jie Shen.
• 08/2015 -- 03/2016: Visiting Scholar, School of Mathematical Science, Peking University.

Research Interests

• Modeling and simulation of liquid crystals
• Numerical methods for gradient flows
• Interfaces between ordered structures

Publications

• (With Hanbin Wang and Zhiguo Yang) A second-order $SO(3)$-preserving and energy-stable scheme for orthonormal frame gradient flow model of biaxial nematic liquid crystals, Journal of Scientific Computing, 99, 75(2024).
• (With Xiaotian Yang and Zhiguo Yang) A second-order length-preserving and unconditionally energy stable rotational discrete gradient method for Oseen-Frank gradient flows , Communications in Computational Physics, 35(2), 369-394(2024).
• (With Sirui Li and Chenchen Wang) Uniqueness of global weak solutions to the frame hydrodynamics for biaxial nematic phases in $\mathbb{R}^2$, Communications in Mathematical Sciences, 22(2), 461-485(2024).
• (With Sirui Li) Rigorous biaxial limit of a molecular-theory-based two-tensor hydrodynamics, Journal of Differential Equations, 366, 862-911(2023).
• (With Sirui Li) Frame hydrodynamics of biaxial nematics from molecular-theory-based tensor models, SIAM Journal on Applied Mathematics, 83(4), 1467-1495(2023).
• (With Yanli Wang) $Q$-tensor gradient flow with quasi-entropy and discretizations preserving physical constraints, Journal of Scientific Computing, 94, 9(2023).
• (With Kai Jiang and Wei Si) Tilt grain boundaries of hexagonal structures: a spectral viewpoint, SIAM Journal on Applied Mathematics, 82(4), 1267-1286(2022).
• (With Xiaomei Yao and Lei Zhang) Transition pathways in cylinder-gyroid interface, Communications in Computational Physics, 32(3), 810-828(2022).
• Quasi-entropy by log-determinant covariance matrix and application to liquid crystals, Physica D: Nonlinear Phenomena, 435, 133308(2022).
• Symmetry-consistent expansion of interaction kernels between rigid molecules, CSIAM Transactions on Applied Mathematics, 3(3), 383-427(2022).
• (With Jie Shen) Unconditionally positivity preserving and energy dissipative schemes for Poisson--Nernst--Planck equations, Numerische Mathematik, 148, 671-697(2021).
• (With Duo Cao and Jie Shen) Computing interface with quasiperiodicity, Journal of Computational Physics, 424, 109863(2021).
• (With Jeff Z. Y. Chen) General liquid-crystal theory for anisotropically shaped molecules: symmetry, orientational order parameters, and system free energy, Physical Review E, 102(6), 062701(2020).
• Classifying local anisotropy formed by rigid molecules: symmetries and tensors, SIAM Journal on Applied Mathematics, 80(6), 2518-2546(2020).
• (With Jie Shen) Unconditionally bound preserving and energy dissipative schemes for a class of Keller-Segel equations, SIAM Journal on Numerical Analysis, 58(3), 1674-1695(2020).
• (With Jie Shen and Jiang Yang) A new class of efficient and robust energy stable schemes for gradient flows, SIAM Review, 61(3), 474-506(2019).
• (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).
• (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).
• (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).
• (With Jie Shen and Pingwen Zhang) Approximations on SO(3) by Wigner D-matrix and applications, Journal of Scientific Computing, 74(3), 1706-1724(2018).
• (With Yixiang Luo and Pingwen Zhang) A fast algorithm for the moments of Bingham distribution, Journal of Scientific Computing, 75(3), 1337-1350(2018).
• (With Pingwen Zhang) Calculating elastic constants of bent-core molecules from Onsager-theory-based tensor model, Liquid Crystals, 45(1), 22-31(2018).
• (With Jie Shen and Jiang Yang) The scalar auxiliary variable (SAV) approach for gradient flows, Journal of Computational Physics, 353, 407-416(2018).
• (With Jie Shen) Stabilized predictor-corrector schemes for gradient flows with strong anisotropic free energy, Communications in Computational Physics, 24(3), 635-654(2018).
• (With Chu Wang, An-Chang Shi and Pingwen Zhang) Computing optimal interfacial structure of modulated phases, Communications in Computational Physics, 21, 1-15(2017).
• (With Pingwen Zhang) The transmission of symmetry in liquid crystals, Communications in Mathematical Sciences, 15(1), 185-195(2017).
• (With Pingwen Zhang) From microscopic theory to macroscopic theory: symmetries and order parameters of rigid molecules, Science China Mathematics, 57, 443-468(2014).

Preprints

• (With Sirui Li and Chenchen Wang) Well-posedness of frame hydrodynamics for biaxial nematic liquid crystals, arXiv:2202.08998.

Package

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

Past teachings

• Spring 2017/2018/2019, Ordinary Differential Equations, Purdue University.
• Summer 2023, Gradient flow models and numerical methods, CAS.