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A structure-preserving finite element discretization for the time-dependent Nernst-Planck equation 期刊论文
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2021, 页码: 20
Authors:  Zhang, Qianru;  Tu, Bin;  Fang, Qiaojun;  Lu, Benzhuo
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Structure-preserving finite element discretization  Nernst-Planck equation  Scharfetter-Gummel approximation  Jordan-Kinderlehrer-Otto scheme  
Unconditionally positivity preserving and energy dissipative schemes for Poisson-Nernst-Planck equations 期刊论文
NUMERISCHE MATHEMATIK, 2021, 页码: 27
Authors:  Shen, Jie;  Xu, Jie
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65M12  35K61  35K55  65Z05  70F99  
ANALYSIS OF THE MEAN FIELD FREE ENERGY FUNCTIONAL OF ELECTROLYTE SOLUTION WITH NONHOMOGENOUS BOUNDARY CONDITIONS AND THE GENERALIZED PB/PNP EQUATIONS WITH INHOMOGENEOUS DIELECTRIC PERMITTIVITY 期刊论文
SIAM JOURNAL ON APPLIED MATHEMATICS, 2018, 卷号: 78, 期号: 2, 页码: 1131-1154
Authors:  Liu, Xuejiao;  Qiao, Yu;  Lu, Benzhou
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free energy functional  electrolyte  boundary conditions  variable dielectric  generalized Poisson-Nernst-Planck/Poisson-Boltzmann equations  energy law  
MODIFIED POISSON-NERNST-PLANCK MODEL WITH ACCURATE COULOMB CORRELATION IN VARIABLE MEDIA 期刊论文
SIAM JOURNAL ON APPLIED MATHEMATICS, 2018, 卷号: 78, 期号: 1, 页码: 226-245
Authors:  Liu, Pei;  Ji, Xia;  Xu, Zhenli
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charge transport  ion correlation  continuum theory for electrostatics  asymptotic expansion  Green's function  Poisson-Nernst-Planck equations  
A Local Approximation of Fundamental Measure Theory Incorporated into Three Dimensional Poisson-Nernst-Planck Equations to Account for Hard Sphere Repulsion Among Ions 期刊论文
JOURNAL OF STATISTICAL PHYSICS, 2016, 卷号: 163, 期号: 1, 页码: 156-174
Authors:  Qiao, Yu;  Liu, Xuejiao;  Chen, Minxin;  Lu, Benzhuo
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Hard sphere repulsion  Three dimensional fundamental measure theory  Poisson-Nernst-Planck equations  Size-modified PNP  Equation of state  
Poisson-Nernst-Planck equations for simulating biomolecular diffusion-reaction processes I: Finite element solutions 期刊论文
JOURNAL OF COMPUTATIONAL PHYSICS, 2010, 卷号: 229, 期号: 19, 页码: 6979-6994
Authors:  Lu, Benzhuo;  Holst, Michael J.;  McCammon, J. Andrew;  Zhou, Y. C.
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Electrodiffusion  Poisson-Nernst-Planck equations  Finite element  Singular charges  Molecular surface  Boundary condition  Conditioning