Research Interests:
Mathematical modeling of fluid systems and electrophysiology
Fast algorithms for partial differential equations and integral equations
Integral equation theory and classical density functional theory in complex fluids
Kinetic theory and its application in fluid dynamics
Publications:
C.-Y. Hsieh, T.-C. Lin, C. Liu, P. Liu, Global Existence of the Non-isothermal Poisson-Nernst-Planck-Fourier System. Submitted (2020).
J. Liang, P. Liu, Z. Xu, A fast Poisson solver of arbitrary order accuracy through the harmonic surface mapping algorithm. Submitted (2020).
Y. Wang, C. Liu, P. Liu, B. Eisenberg, Field theory of reaction-diffusion: Mass action with an energetic variational approach . Submitted (2020).
P. Liu, S. Wu and C. Liu, Non-Isothermal Electrokinetics: Energetic Variational Approach. Comm. Math. Sci., 5 (2018), pp. 1451–1463.
Q. Zhao , P. Liu and Z. Xu, A fast method for evaluating Green's function in irregular domains with application to charge interaction in a nanopore. Commun. Comput. Phys., 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 J. Appl. Math., 78(3): 1802--1822, 2018.
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. Polym. Chem.,8: 5673--5678, 2017.
P. Liu, X. Ji and Z. Xu, Modified Poisson-Nernst-Planck model with accurate Coulomb correlation in variable media. SIAM J. Appl. Math., 78(1), 226--245, 2017.
P. Liu, C. Liu and Z. Xu, Generalized Shockley-Ramo Theorem in electrolytes . Comm. Math. Sci., 15(2): 555--564, 2017.
P. Liu, M. Ma and Z. Xu, Understanding depletion induced like-charge attraction from self-consistent field model. Comm. Comp. Phys., 22(1): 95--111, 2017.
Z. Xu, M. Ma and P. Liu, Self-energy modified Poisson-Nernst-Planck equations: WKB approximation and finite-difference approaches. Phys. Rev. E., 90(1), 013307, 2014.
B. Li, P. Liu, S. Zhou and Z. Xu, Ionic size effects: Generalized Boltzmann distributions, counterion stratification, and modified Debye length. Nonlinearity, 26(10): 2899--2922, 2013. Selected in the journal's Highlights of 2013.