My research area is in Applied Mathematics, with a focus on mathematical modeling, model reduction and numerical methods.
If you are a highly-motivated undergraduate student looking for a capstone project advisor, please feel free to contact me.
I am also looking for hightly-motivated graduate students.
- BS, Mathematics, Shanghai Jiao Tong University, 2012
- BS, Physics, Shanghai Jiao Tong University, 2012
- PhD, Applied Mathematics, Shanghai Jiao Tong University, 2017
- Postdoctor, School of Mathematics, University of Minnesota, Twin-Cities. 2019 – 2022
- Postdoctor, Department of Mathematics, The Pennsylvania State University, University Park, 2017 - 2019
- MTH3312: Scientific Computing
- MTH4311: Numerical Analysis
- X. Ji, C. Liu; P. Liu, S. Zhou, Energetic Variational Approach for Prediction of Thermal Electrokinetics in Charging and Discharging Processes of Electrical Double Layer Capacitors, Journal of Power Sources, 2022.
- P. Liu, J. Arsuaga, M. C. Calderer, D. Golovaty, M. Vazquez, S. Walker, Helical organization of DNA-like liquid crystal filaments in cylindrical viral capsids, Proceedings of the Royal Society A, 478 (2022), 20220047.
- P. Liu, J. Arsuaga, M. C. Calderer, D. Golovaty, M. Vazquez, S. Walker, Ion-dependent DNA Configuration in Bacteriophage Capsids, Biophysical Journal, 120 (2021), pp. 3292–3302.
- J. Liang, P. Liu, Z. Xu, A high-accurate fast Poisson solver based on harmonic surface mapping algorithm, Communications in Computational Physics, 30 (2021), pp. 210–226.
- Y. Wang, C. Liu, P. Liu, B. Eisenberg, Field Theory of Reaction-Diffusion: Law of Mass Action with an Energetic Variational Approach, Physical Review E, 102 (2020), 062147.
- C.-Y. Hsieh, T.-C. Lin, C. Liu and P. Liu, Global existence of the non-isothermal Poisson–Nernst–Planck–Fourier system, Journal of Differential Equations, 269(2020), pp. 7287–7310.
- P. Liu, S. Wu and C. Liu, Non-Isothermal Electrokinetics: Energetic Variational Approach, Communication in Mathematical Sciences, 5 (2018), pp. 1451–1463.
- Q. Zhao, P. Liu and Z. Xu, A fast method for evaluating greens function in irregular domains with application to charge interaction in a nanopore, Communications in Computational Physics, 24 (2018), pp. 1241–1258.
- L. Ji, P. Liu, Z. Xu and S. Zhou, Asymptotic analysis on dielectric boundary effects of modified Poisson–Nernst–Planck equations, SIAM Journal on Applied Mathematics, 78 (2018), pp. 1802–1822.
- P. Liu, X. Ji and Z. Xu, Modified Poisson–Nernst–Planck model with accurate Coulomb correlation in variable media, SIAM Journal on Applied Mathematics, 78 (2018), pp. 226–245.
- Z. Wu∗, P. Liu, Y. Liu, W. Wei, X. Zhang, P. Wang, Z. Xu and H. Xiong, Regulating sequence distribution of polyethers via ab initio kinetics control in anionic copolymerization, Polymer Chemistry, 8 (2017), pp. 5673–5678.
- P. Liu, C. Liu and Z. Xu, Generalized Shockley–Ramo Theorem in electrolytes, Communication in Mathematical Sciences, 15 (2017), pp. 555–564.
- P. Liu, M. Ma and Z. Xu, Understanding depletion induced like-charge attraction from self-consistent field model, Communications in Computational Physics, 22 (2017), pp. 95–111.
- Z. Xu, M. Ma and P. Liu, Self-energy modified Poisson–Nernst–Planck equations: WKB approximation and finite-difference approaches, Physics Review E, 90 (2014), 013307.
- B. Li, P. Liu, S. Zhou and Z. Xu, Ionic size effects: Generalized Boltzmann distributions, counterion stratification, and modified Debye length, Nonlinearity, 26 (2013), pp. 2899–2922.
- Mathematical modeling and analysis of complex fluid systems, such as the liquid crystals and electrolytes.
- Numerical analysis and fast algorithms for partial differential equations and integral equations.
- Asymptotic analysis and special functions.
- Applications in energy devices, for example, the energy efficiency and charging dynamics of batteries.
- Applications in biology, for example, configuration of bacteriophage DNA, charge transport and conformational changes in ion channels.