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Some corrections

Book/chapter

  1. Benzhuo Lu, Poisson-Nernst-Planck equation, in book: Encyclopedia of Applied and Computational Mathematics, edited by Bjorn Engquist, Publisher: Springer-Verlag: Berlin Heidelberg, 2013.
  2. Benzhuo Lu, Finite Element Modeling of Biomolecular Systems in Ionic Solution，in book：Image-Based Geometric Modeling and Mesh Generation. Publisher：Springer Berlin Heidelberg, 2013, XI, p271.
  3. Minxin Chen, Bin Tu，and Benzhuo Lu，Surface Triangular Mesh and Volume Tetrahedral Mesh Generations for Biomolecular Modelling，in book：Image-Based Geometric Modeling and Mesh Generation. Publisher：Springer Berlin Heidelberg, 2013, XI, p85-106.

Invited Review

  1. B. Z. Lu, Y. C. Zhou, Michael J. Holst, and J. A. McCammon. Recent progress in numerical methods for the Poisson-Boltzmann equation in biophysical applications. Commun. in Comput. Phys., 3(5):973-1009, 2008. (PDF), link to the Journal webpage .

( Top 10 most cited paper of this journal [till 05/2010], see the journal webpage)

  1. Minxin Chen, and B. Z. Lu, Advances in biomolecular surface meshing and its applications to mathematical modeling, Chinese Science Bulletin, 58(16):1843-1849, 2013 (PDF)
  2. 彭波，李翰林，卢本卓，生物分子模拟中的静电计算，计算物理，2:127-159, 2015. (PDF)
  3. Qiao Yu, and Lu Ben-Zhuo, Improvements in continuum modeling for biomolecular systems, Chinese Physics B, 25(1): 018705, 2016
  4. 张林波, 郑伟英, 卢本卓, 崔涛, 冷伟,林灯,并行自适应有限元软件平台 PHG 及其应用,中国科学: 信息科学 46:1442, 2016.(PDF)
  5. Gui S, Khan D, Wang Q, Yan D, Lu B., Frontiers in biomolecular mesh generation and molecular visualization systems, Visual Computing for Industry, Biomedicine, and Art, 1:7,2018

Special issue：《数值计算与计算机应用》杂志专刊“半导体器件及其辐射损伤效应数值模拟方法与软件”，前言及三篇文章：

1. 卢本卓，前言，数值计算与计算机应用，41（2）：83-84,2020（PDF）

2. 王芹，马召灿，白石阳，张林波，卢本卓，李鸿亮，三维半导体器件漂移扩散模型的并行有限元方法研究，数值计算与计算机应用，41（2）：85-104,2020 （PDF）（挑战计划，重点研发，NSFC 11771435）

Wang Qin, Ma Zhaocan, Bai Shiyang, Zhang Linbo, Lu Benzhuo, Li Hongliang, RESEARCH ON PARALLEL FINITE ELEMENT METHODS FOR THE DRIFT-DIFFUSION MODEL IN SEMICONDUCTOR DEVICE SIMULATIONS, J. on Numerical Methods and Computer Applications, 41(2）：84-104,2020

3. 马召灿，许竞劼，卢本卓，李鸿亮，半导体器件电离辐照损伤效应模拟的数值算法及应用，数值计算与计算机应用，41（2）：105-120,2020 （PDF）（挑战计划，重点研发，NSFC 11771435）

Ma Zhaocan, Xu Jingjie, Lu Benzhuo, Li Hongliang, NUMERICAL ALGORITHM AND APPLICATION IN SIMULATION OF RADIATION DAMAGE EFFECTS ON SEMICONDUCTOR DEVICES，J. on Numerical Methods and Computer Applications, 41(2）：105-120,2020

4. 黄成梓，白石阳，王芹，马召灿，张倩茹，刘田田，桂升，卢本卓，陈旻昕，李鸿亮，3Ddevice: 半导体器件及其辐照损伤效应仿真软件系统，数值计算与计算机应用，41（2）：121-142,2020 （PDF）（挑战计划，重点研发，NSFC 11771435）

Huang Chengzi, Bai Shiyang, Wang Qin, Ma Zhaocan, Zhang Qianru, Liu Tiantian, Gui Sheng, Lu Benzhuo, Chen Minxin, Li Hongliang, 3DDEVICE: A SIMULATION SOFTWARE SYSTEM FOR SEMICONDUCTOR DEVICES AND RADIATION EFFECTS, J. on Numerical Methods and Computer Applications, 41(2）：121-142,2020

Research Articles

Machine learning （机器学习）：

1. 吕敏瑞，视频身份验证问题中的特征设计和算法分析, （指导老师 卢本卓） 毕业论文，中国科学院大学，2020

2. Gui S, Chen Z, Lu B, Chen M. Molecular Sparse Representation by 3D Ellipsoid Radial Basis Function Neural Network via L1 Regularization, J. Chemical Information and Modeling, 60: 6054-6064, 2020 (PDF) （支持：重点研发2016YF-B0201304, NSFC 11771435 and NSFC 21573274）

3. Wenxuan Zhang, Benzhuo Lu, Stock Trend Prediction with Machine Learning: Incorporating Inter-Stock Correlation Information through Laplacian Matrix, Big Data Cogn. Comput., 8(6):56, 2024 (PDF) (支持，NSFC 11771435, 22073110, 先导 No. XDB0500000)

 

Computational biology/nanopore/semicondutor device (计算生物/纳米孔/半导体器件方向/计算金融)：

  1. Sheng Gui, Benzhuo Lu, Weilin Yu, Ion transport in a dipolar media I: a local dielectric Poisson-Nernst-Planck/Poisson-Boltzmann model, SIAM J Appl. Math., 84(5), 2110--2131, 2024 (PDF) (支持，先导 No. XDB0500000, NSFC 12371413, 22073110)
  2. Ruigang Shen, Qianru Zhang, and Benzhuo Lu, An Inverse Averaging Finite Element Method for Solving the Size-Modified Poisson-Nernst-Planck Equations in Ion Channel Simulations, Commun. Comput. Phys., 36(2), 521-550, 2024 (PDF) (支持, NSFC 12371413, 22073110)
  3. Naveed Ahmad Khan, Muhammad Sulaiman, Benzhou Lu, ANN based optimization of nano-beam oscillations with intermolecular forces and geometric nonlinearity, International Journal of Solids and Structures , 304, 113054, 2024 (PDF)
  4. Naveed Ahmad Khan, Muhammad Sulaiman, Benzhou Lu, Predictive insights into nonlinear nanofluid flow in rotating systems: a machine learning approach, Engineering with Computers, xx, 2024 (PDF)
  5. Ziyang Liu, Sheng Gui, Benzhuo Lu, Linbo Zhang, An Unfitted Finite Element Poisson–Boltzmann Solver with Automatic Resolving of Curved Molecular Surface, J. Phys. Chem. B, 128, 6463−6475, 2024 (PDF) (支持，先导 No. XDB0500000, NSFC 12371413, 22073110)
  6. Sidi Wu, Aiqing Zhu, Yifa Tang, Benzhuo Lu, Solving parametric elliptic interface problems via interfaced
    operator network, J. Comput. Phys., 514, 113217, 2024 (PDF) (支持，先导 No. XDB0500000, NSFC 12371413, 22073110)
  7. Minrui Lv, Benzhuo Lu, A flux-based moving mesh method applied to solving the
    Poisson–Nernst–Planck equations, J. Comput. Phys., 513, 113169, 2024 (PDF) (支持，先导 No. XDB0500000, NSFC 12371413, 22073110)
  8. Wenxuan Zhang, Benzhuo Lu, Stock Trend Prediction with Machine Learning: Incorporating Inter-Stock Correlation Information through Laplacian Matrix, Big Data Cogn. Comput., 8(6):56, 2024 (PDF) (支持，NSFC 11771435, 22073110, 先导 No. XDB0500000)
  9. Keying Ma, Jianbo Lu, and Benzhuo Lu, Parameter-Efficient Densely Connected Dual Attention Network for Phonocardiogram Classification, IEEE Journal of Biomedical and Health Informatics, 27(9), 4240-4249, 2023 (PDF) (支持，NSFC 11771435, 22073110)
  10. Sidi Wu, Aiqing Zhu, Yifa Tang, Benzhuo Lu, Convergence of Physics-Informed Neural Networks Applied to Linear Second-Order Elliptic Interface Problems, Commun. Comput. Phys., 33, 596-627, 2023 (PDF) (支持，NSFC 11771435, 22073110)
  11. Zhen Chao, Sheng Gui, Benzhuo Lu, Dexuan Xie, EFFICIENT GENERATION OF MEMBRANE AND SOLVENT TETRAHEDRAL MESHES FOR ION CHANNEL FINITE ELEMENT CALCULATION, INTERNATIONAL J NUMERICAL ANALYSIS AND MODELING, 19(6), 887-906, 2022 (PDF) (支持，NSFC 11771435, 22073110)
  12. Sidi Wu, Benzhuo Lu, INN: Interfaced neural networks as an accessible meshless approach for solving interface PDE problems, J. Comput. Phys., 470, 111588, 2022 (PDF) (支持，NSFC 11771435, 22073110)
  13. 倪宇晖，张倩茹，王芹，阳莺，卢本卓，SPNP晶体管辐照损伤效应的有限元数值模拟，数值计算与计算机应用，43（3）：237-247,2022 （PDF）（挑战计划，NSFC 11771435，22073110）
  14. Qianru Zhang, Qin Wang, Linbo Zhang, Benzhuo Lu, A class of finite element methods with averaging techniques for solving the three-dimensional drift-diffusion model in semiconductor device simulations, J. Comput. Phys., 458, 111086, 2022 (PDF) (支持，NSFC 11771435, 22073110，ZLB的重点研发Nos. 2019YFA0709600 and 2019YFA0709601)
  15. Qianru Zhang, Qin Wang, Linbo Zhang, Benzhuo Lu， An inverse averaging finite element method for solving three-dimensional Poisson–Nernst–Planck equations in nanopore system simulations， J.Chem. Phys., 155, 194106, 2021   (PDF) (支持，NSFC 11771435, 22073110，ZLB的重点研发)
  16. Qianru Zhang, Bin Tu, Qiaojun Fang,  Benzhuo Lu, A structure-preserving finite element discretization for the time-dependent Nernst-Planck equation, J. Appl. Math. Comput. 68: 1545–1564, 2022. (PDF) (支持，重点研发，NSFC 11771435, 22073110)
  17. Jinyong Ying, Ronghong Fan, Jiao Li, Benzhuo Lu， A new block preconditioner and improved finite element solver of Poisson-Nernst-Planck equation， J.Comput. Phys., 430:110098, 2021. (PDF) (支持，重点研发，NSFC 11771435, 22073110)
  18. Shuhua Hou, Qianru Zhang, Zhen Zhang, Xiangyu Kong, Benzhuo Lu, Liping Wen, Lei Jiang, Charged porous asymmetric membrane for enhancing salinity gradient energy conversion, Nano Energy, 79：105509, 2021 . (PDF) (支持，重点研发，NSFC 11771435)
  19. Weipeng Chen, Qianru Zhang, Yongchao Qian, Weiwen Xin, Dezhao Hao, Xiaolu Zhao, Congcong Zhu, Xiangyu Kong, Benzhuo Lu, Lei Jiang, and Liping Wen, Improved Ion Transport in Hydrogel-Based Nanofluidics for Osmotic Energy Conversion， ACS Cent. Sci. 6: 2097-2104，2020. （PDF）（重点研发，NSFC 21573274,11771435)
  20. Wanwan Zhu, Ying Yang, Guanghua Ji, Benzhuo Lu, Residual type a posteriori error estimates for the time-dependent Poisson-Nernst-Planck equations, J Scientific Computing, 90:27, 2022. (PDF) (挑战计划，重点研发，NSFC 21573274,11771435)
  21. Ying Yang, Ming Tang, Chun Liu, Benzhuo Lu, LiuQiang Zhong, Superconvergent Gradient Recovery for Nonlinear Poisson-Nernst-Planck equations with Applications to the Ion Channel Problem, Advances in computational mathematics, 46: 78，2021. （PDF）（重点研发，挑战计划（第二），NSFC 11771435）
  22. DEXUAN XIE, AND BENZHUO LU, An Effective Finite Element Iterative Solver for a Poisson-Nernst-Planck Ion Channel Model with Periodic Boundary Conditions, SIAM J Sci. Computing., 42（6）：B1490--B1516, 2020. (PDF) (支持：重点研发 2016YFB0201304, 挑战计划， NSFC 11771435, 22073110)
  23. 马召灿，李鸿亮，卢本卓，多组分漂移-扩散-反应非线性模型的高性能并行算法及其在电离损伤效应中的应用，太赫兹科学与电子信息学报（已接收），19(6)：xxx, 2021 (挑战计划)
  24. 王芹，马召灿，李鸿亮，张林波，卢本卓，双极器件LPNP 辐照损伤效应的并行有限元数值模拟，系统仿真学报，32(12)：2376-2382， 2020 （PDF）(挑战计划,国家重点研发计划，NSFC 21573274, 11771435)
  25. Qin Wang, Hongliang Li, Linbo Zhang, Benzhuo Lu, A stabilized finite element method for the Poisson–Nernst–Planck equations in three-dimensional ion channel simulations, Applied Mathematics Letters, 111: 106652, 2021 (PDF)(挑战计划，重点研发，NSFC 21573274,11771435)
  26. Weipeng Chen,⊥ Qin Wang,⊥ Jianjun Chen, Qianru Zhang, Xiaolu Zhao, Yongchao Qian, Congcong Zhu, Linsen Yang, Yuanyuan Zhao, Xiang-Yu Kong, Benzhuo Lu, Lei Jiang, and Liping Wen, Improved Ion Transport and High Energy Conversion through Hydrogel Membrane with 3D Interconnected Nanopores, Nano Lett. 20: 5705-5713, 2020 (PDF) (重点研发#3，NSFC 21573274,11771435)
  27. Qianru Zhang, Sheng Gui, Hongliang Li, Benzhuo Lu, Model reduction-based initialization methods for solving the Poisson-Nernst-Plank equations in three-dimensional ion channel simulations, J. Computational Physics, 419: 109627, 2020 (PDF) (挑战计划，重点研发，NSFC 21573274,11771435)
  28. Weifeng Zhang, Ronghong Fan, Liuqiang Zhong, Iterative two-grid methods for semilinear elliptic equations, Computers & Mathematics with Applications, 80(3): 522-530, 2020 (挑战计划 第一)
  29. Ruigang Shen， Shi Shu， Ying Yang， Benzhuo Lu， A decoupling two-grid method for the time-dependent Poisson-Nernst-Planck equations， Numerical Algorithms，83(4): 1613–1651, 2020. (PDF) (第三之后的支持：挑战计划，重点研发，NSFC 21573274,11771435)）
  30. Hao Dong, Yiming Zhang, Ruiheng Song, Jingjie Xu, Yigao Yuan, Jindou Liu, Jia Li, Sisi Zheng, Tiantian Liu， Benzhuo Lu, Youjun Wang, and Michael L. Klein， Toward a Model for Activation of Orai Channel, iScience, 16: 356–367, 2019 (PDF) (支持：重点研发，NSFC 21573274)
  31. Ying Yang, Benzhuo Lu, Yan Xie, A DECOUPLING TWO-GRID METHOD FOR THE STEADY-STATE POISSON-NERNST-PLANCK EQUATIONS, J. Computational Mathematics, 37: 556–578, 2019 (PDF) (支持：挑战计划，重点研发，NSFC 21573274,11771435)
  32. Jiao Li, Jinyong Ying, Benzhuo Lu, A flux-jump preserved gradient recovery technique for accurately predicting the electrostatic field of an immersed biomolecule, J. Comput. Phys. 396: 193-208, 2019 (PDF) (支持：挑战计划 TZ2016003, 重点研发，NSFC 21573274，11771435)
  33. B. Zhang, J. DeBuhr, D. Niedzielski, S. Mayolo, B. Lu, T. Sterling, DASHMM Accelerated Adaptive Fast Multipole Poisson-Boltzmann Solver on Distributed Memory Architecture, Computer Phys Commun. 25: 1235-1258, 2019 (PDF) (支持：挑战计划 TZ2016003, NSFC 21573274)

    (* High performance parallel boundary element PB solver, tested up to tens of thousands cores )

  34. Yu Qiao, Cheng Lian, Benzhuo Lu, Jianzhong Wu, Modeling selective ion adsorption into cylindrical nanopores, Chemical Physics Letters, 709：116-124，2018. （PDF） (支持：挑战计划，重点研发，NSFC 21573274,11771435)
  35. Xuejiao Liu, Yu Qiao, and Benzhuo Lu, Analysis of the Mean Field Free Energy Functional of Electrolyte Solution with Non-homogenous Boundary Conditions and the Generalized PB/PNP Equations with Inhomogeneous Dielectric Permittivity, SIAM J Appl. Math. 78(2): 1131-1154, 2018. （PDF）(支持：挑战计划，NSFC 21573274, NSFC 91530102)
  36. Tiantian Liu, M.X. Chen, and B.Z. Lu, Efficient and qualified mesh generation for Gaussian molecular surface using adaptive partition and piecewise polynomial approximation, SIAM J Sci. Computing., 40(2): B507-B527, 2018. (PDF) (支持：挑战计划，重点研发 2016YFB0201304, NSFC 21573274, NSFC 91530102)
  37. Bin Tu, Shiyang Bai, Benzhuo Lu, Qiaojun Fang, Conic shapes have higher sensitivity than cylindrical ones in nanopore DNA sequencing, Scientific Reports, 8:9097, 2018 (重点研发 2016YFB0201304, NSFC 21573274 and 11771435)
  38. Jingjie Xu, Benzhuo Lu, and Linbo Zhang, A Time-Dependent Finite Element Algorithm for Simulations of Ion Current Rectification and Hysteresis Properties of 3D Nanopore System，IEEE Transactions on Nanotechnology, 17(3):513-519, 2018 （支持：挑战计划，重点研发，NSFC 21573274,11771435）
  39. Dawar Khan, Dong-Ming Yan, Sheng Gui, Benzhuo Lu and Xiaopeng Zhang, Molecular Surface Remeshing with Local Region Refinement, Int. J. Mol. Sci. 19: 1383, 2018.（支持：挑战计划，重点研发，NSFC 21573274,11771435）
  40. Nan Ji, Tiantian Liu, Jingjie Xu, Longzhu Q. Shen and Benzhuo Lu, A Finite Element Solution of Lateral Periodic Poisson–Boltzmann Model for Membrane Channel Proteins, Int. J. Mol. Sci. 19(3)： 695, 2018. (link) (支持：重点研发，挑战计划，NSFC 21573274,11771435)
  41. Longzhu Shen, Nan Ji, Benzhuo Lu, Introducing Membrane Transport Energy into the Design of Sustainable Chemicals against Cytotoxicity, ACS Sustainable Chemistry & Engineering,6:2055-2061, 2018. （PDF）（支持：重点研发 2016YFB0201304, NSFC 21573274）
  42. Xuejiao Liu and Benzhuo Lu, Incorporating Born Solvation Energy into the 3D Poisson-Nernst-Planck Model to Study Ion Selectivity in KcsA K+ Channels, Phys. Rev. E, 96: 062416， 2017 （PDF）(支持：重点研发 2016YFB0201304, 挑战计划， NSFC 21573274，11771435)
  43. Beibei Huang, Xuejiao Liu, Zhi Tan, Benzhuo Lu, and Shuxing Zhang, Interaction between Charged Cylinders in Electrolyte Solution via Variable
    Dielectric Poisson-Boltzmann Model, Phys. Rev. E, (submitted), 2017 (挑战计划 TZ2016003, NSFC 21573274)

  44. Jingjie Xu, Zhaocan Ma, Hongliang Li, Yu Song, Linbo Zhang, and Benzhuo Lu, A Multi-Time-Step Finite Element Algorithm for 3D Simulation of Coupled Drift-Diffusion-Reaction Process in Total Ionizing Dose Effect, IEEE Transactions on Semiconductor Manufacturing, 31(1): 183-189, 2018 (PDF) (支持：挑战计划，2016YFB0201304, NSFC 21573274，11771435)
  45. Liu T, Chen M, Song Y, Li H, Lu B, Quality improvement of surface triangular mesh using a modified Laplacian smoothing approach avoiding intersection. PLoS ONE, 12(9): e0184206, 2017. (PDF) (支持：挑战计划 TZ2016003, NSFC 21573274)
  46. Zhaocan Ma, Jingjie Xu, Hongliang Li, Song Yu, Linbo Zhang, and Benzhuo Lu, 3D Simulation of the Defect Generation by Hydrogen at Si-SiO2 Interface, Proceedings of the International Conference on Computational Methods, Vol.4: 610, 2017 (支持：挑战计划 TZ2016003, NSFC 21573274，11771435)
  47. 路建波，高华方，张世华，卢本卓，马旭，缺失数据下蛋白质多结构叠加的迭代方法，中国生物化学与分子生物学报，33(6):630-637，2017 （PDF）（NSFC 21573274）
  48. 路建波，高华方，卢本卓，马旭，基于高斯曲率的蛋白质嵌入到对称低温电镜密度图的方法，北京工业大学学报，43:1881-1887，2017 （PDF） （NSFC 21573274）
  49. 路建波，张世华，马旭，卢本卓，一种基于特征点匹配的生物大分子装配方法，数值计算与计算机应用，38:155-166，2017 （PDF） （NSFC 21573274）

  50. Jianbo Lu, Guoliang Xu, Shihua Zhang, and Benzhuo Lu, An effective sequence-alignment-free superpositioning of pairwise or multiple structures with missing data, Algorithms for Molecular Biology, 11:18, 2016. (PDF)
  51. Jingjie Xu, Yan Xie, Benzhuo Lu, and Linbo Zhang, Charged Substrate and Product Together Contribute Like a Nonreactive Species to the Overall Electrostatic Steering in Diffusion-Reaction Processes, J. Phys. Chem. B, 120: 8147-8153, 2016. (PDF)

    52. (* Explain: why the charged substrate and product are not explicitly considered in the Debyle-Huckel limiting law )

  52. Yu Qiao, Xuejiao Liu, Minxin Chen, Benzhuo Lu, A Local Approximation of Fundamental Measure Theory Incorporated into Three Dimensional Poisson–Nernst–Planck Equations to Account for Hard Sphere Repulsion Among Ions, Journal of Statistical Physics, 163(1): 156-174, 2016. (PDF)

    53. (* FMT + PNP, size effects, Monte Carlo simulation, equation of state)

  53. 许竞劼, 谢妍, 卢本卓, 一个基于PHG平台的并行有限元生物分子模拟解法器, 数值计算与计算机应用, 37(1):67-82, 2016. (PDF)
  54. Yan Xie,Tiantian Liu,Bin Tu, Benzhuo Lu, Linbo Zhang, Automated Parallel and Body-fitted Mesh Generation in Finite Element Simulation of Macromolecular Systems, Commun. in Comput. Phys.,19: 582-602, 2016. (PDF)
  55. Tiantian Liu, Shiyang Bai, Bin Tu, Minxin Chen, Benzhuo Lu, Membrane-Channel Protein System Mesh Construction for Finite Element Simulations, Molecular Based Mathematical Biology, 3: 128-139, 2015. (pdf)
  56. T.T. Liu, M.X. Chen, B.Z. Lu, Parameterization for molecular Gaussian surface and a comparison study of surface mesh generation, J. Molecular Modeling, 21(5):113, 2015. (PDF)
  57. Bo Zhang, Bo Peng, Jingfang Huang, Nikos P. Pitsianis, Xiaobai Sun, Benzhuo Lu, Parallel AFMPB solver with automatic surface meshing for calculations of molecular solvation free energy, Computer Physics Communications, 190: 173–181, 2015. (PDF)

    58. ( * Parallel AFMPB using Cilk Plus, C and fortran mixed, total solvation energy calculation, automeshing (VDW surface) as an option )

  58. Bin Tu, Yan Xie, Linbo Zhang, Benzhuo Lu, Stabilized finite element methods to simulate the conductances of ion channels, Computer Physics Communications, 188: 131-139, 2015 (PDF).
  59. Hanlin Li and Benzhuo Lu, An ionic concentration and size dependent dielectric permittivity Poisson-Boltzmann model for biomolecular solvation studies, J. Chem. Phys. 141: 024115, 2014 (PDF)

    60. ( * a variable dielectric PB model (VDPB) )

  60. Yu Qiao, Bin Tu and Benzhuo Lu, Ionic size effects to molecular solvation energy and to ion current across a channel resulted from the nonuniform size-modified PNP equations, J. Chem. Phys. 140: 174102, 2014 (PDF)
  61. B Tu, S Y Bai, M X Chen, Y Xie, L B Zhang and B Z Lu，A software platform for continuum modeling of ion channels based on unstructured mesh, Computational Science & Discovery, 7:014002, 2014 (PDF)
  62. Shiyang Bai, Benzhuo Lu, VCMM: A visual tool for continuum molecular modeling, Journal of Molecular Graphics and Modelling, 50: 44-49, 2014. (PDF)
    (*Visualize and analyze molecule, mesh (both unstructured and structured), and simulation data; Interface for solvers and tools)
  63. Xie Y, Tu B, Lu BZ, Zhang LB. Poisson-Boltzmann 方程的并行有限元求解及网格自适应生成，软件学报，2013,24(Suppl.(2)):110-117。（PDF）
  64. Bin Tu, Minxin Chen, Yan Xie, Linbo Zhang, Bob Eisenberg, and Benzhuo Lu, A Parallel Finite Element Simulator for Ion Transport through Three-dimensional Ion Channel Systems, J. Comput. Chem. 34(24): 2065-2078, 2013. (PDF)

    65. Selected as Inside Cover image of JCC (Volume 34, Issue 24).

    ( * Parallel finite element method, ion channel simulation, mesh generation for channel protein and membrane system, comparison with Brownian dynamics simulation and experimental results )

  65. Minxin Chen, Bin Tu, Benzhuo Lu, Triangulated Manifold Meshing Method Preserving Molecular Surface Topology, Journal of Molecular Graphics and Modelling, 38: 411-418, 2012 (PDF).

    66. ( * An improverd version of TMSmesh, aiming to make the generated molecular surface mesh to be a manifold mesh )

  66. Yan Xie, Jie Cheng, Benzhuo Lu, Linbo Zhang, Parallel Adaptive Finite Element Algorithms for Solving the Coupled Electro-diffusion Equations, Molecular Based Mathematical Biology, 1: 90-108, 2013 (pdf).
  67. Ying Yang, B.Z. Lu, An Error Bounds Analysis for the Finite Element Approximation to the Steady-state Poisson-Nernst-Planck equations, Advances in Applied Mathematics and Mechanics, 5(1): 113-130, 2013. (pdf)
  68. Bo Zhang, Benzhuo Lu, Xiaolin Cheng, Jingfang Huang, Nikos P. Pitsianis, Xiaobai Sun, and J. Andrew McCammon, Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver, Commun. in Comput. Phys. 13(1): 107-128, 2013 (PDF).
  69. Beibei Huang, Bin Tu, Benzhuo Lu, A fast direct solver for a class of 3-D elliptic PDE with variable coefficient, Commun. in Comput. Phys. 12(4): 1148-1162, 2012.
  70. Benzhuo Lu, Yongcheng Zhou, Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes II: Size Effects on Ionic Distributions and Diffusion-reaction Rates, Biophysical J. 100(10):2475-2485, 2011 (PDF)

    71. ( * Size-Modified PB, Size-modified Poisson-Nernst-Planck equations, arbitrarily non-uniform sizes, finite size effects on diffusion-reaction rate)

  71. Minxin Chen, Benzhuo Lu, TMSmesh: A robust method for molecular surface mesh generation using a trace technique, J. Chem. Theory Comput., 7:203-212, 2011 (PDF)

    72. ( * Molecular surface meshing tool, being capable of generating mesh for arbitrarily large molecule with good quality in terms of topological correctness, faithfulness to original molecular surface, and uniformness.)

  72. Y. C. Zhou, Benzhuo Lu, and Alemayehu A. Gorfe, Continuum electromechanical modeling of a protein-membrane interaction, Phys. Rev. E 82, 041923 (2010) [5 pages] (PDF)

    73. ( * Electrostatic-elastic (membrane) model, electrostatic force induced membrane curvature )

  73. Benzhuo Lu, Michael J. Holst, J. Andraw McCammon, and Y. C. Zhou. Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes I: Finite Element Solutions, J. Comput. Phys. 2010. 229:6979-6994. (PDF)

    74. ( * FEM solution of PNP equations, condition number issues)

  74. B. Z. Lu, X. Cheng, J. Huang, J. A. McCammon. AFMPB: An Adaptive Fast Multipole Poisson-Boltzmann Solver for Calculating Electrostatics in Biomolecular Systems, Computer Physics Communications, 181: 1150–1160, 2010. (PDF)

    75. (Has been selected for Faculty of 1000 Biology: evaluations for Lu B et al Comput Phys Commun. 2010, 181:1150-60 http://f1000biology.com/article/id/3242956/evaluation )

    (* For AFMPB package description and release )

  75. Bo Li, Benzhuo Lu, Zhongming Wang, J. Andrew McCammon, Solutions to a Reduced Poisson–Nernst–Planck System and Determination of Reaction Rates. Physica A, 389:1329-1345, 2010. (PDF)
  76. Benzhuo Lu, and Andrew McCammon. Kinetics of diffusion-controlled enzymatic reactions with charged substrates. PMC Biophysics, 3:1, 2010. (PDF)
  77. Yong-Woon Jung, Benzhuo Lu, Michael Mascagni. A computational study of ion conductance in the KcsA K+ channel using a Nernst-Planck model with explicit resident ions. J. Chem. Phys. 131, 215101, 2009. (PDF), (jcp link). The article has been selected for the December 2009 issue of JCP: BioChemical Physics. and for the December 15, 2009 issue of the Virtual Journal of Biological Physics Research.
  78. Alemayehu A. Gorfe*, Benzhuo Lu*, Zeyun Yu, and J. Andrew McCammon. Enzymatic Activity versus Structural Dynamics: The Case of Acetylcholinesterase Tetramer. Biophysical Journal., 97(3), 897-905, 2009.(PDF), link to journal.
  79. B. Z. Lu, X. Cheng, J. Huang, J. A. McCammon, An adaptive fast multipole boundary element method for Poisson-Boltzmann electrostatics. J. Chem. Theory Comput., 5(6):1692-1699, 2009. (PDF), link.
  80. Ilja V. Khavrutskii, Alemayehu A. Gorfe, Benzhuo Lu, J. Andrew McCammon. Free Energy for the Permeation of Na+ and Cl- Ions and their Ion-Pair through Zwitterionic Dimyristoyl Phosphatidylcholine Lipid Bilayer by Umbrella Integration with Harmonic Fourier Beads. J. Am. Chem. Soc., 131(5):1706-1716, 2009. (PDF)
  81. B. Z. Lu and J. A. McCammon. Molecular surface-free continuum model for electrodiffusion processes. Chem. Phys. Lett., 451(4-6):282-286, 2008. (PDF)
  82. Y. C. Zhou, B. Z. Lu, Gary A. Huber, Michael J. Holst, and J. A. McCammon. Continuum simulations of acetylcholine consumption by acetylcholinesterase: A Poisson-Nernst-Planck approach. J. Phys. Chem. B, 112(2):270-275, 2008. (PDF)
  83. B. Z. Lu, Y. C. Zhou, Gary A. Huber, Stephen D. Bond, Michael J. Holst, and J. Andrew McCammon. Electrodiffusion: A continuum modeling framework for biomolecular systems with realistic spatiotemporal resolution. J. Chem. Phys., 127(13):135102, 2007. (PDF)
    Also selected for October 15, 2007 issue of Virtual Journal of Biological Physics Research. link
    (* A solver for Poisson-Nernst-Planck, Poisson-Boltzmann, Smoluchowski equations, and realistic spatiotemporal diffusion-reaction problem; hybrid FEM/BEM, surface and volume mesh generation; a bunch of examples )
  84. B. Z. Lu, X. L. Cheng, and J. A. McCammon. "New-Version-Fast-Multipole Method" Accelerated Electrostatic Calculations in Biomolecular Systems. J. Comput. Phys., 226(2):1348-1366, 2007. (PDF)
    (* FMM BEM, technical details )
  85. B. Z. Lu and J. A. McCammon. Improved boundary element methods for Poisson-Boltzmann electrostatic potential and force calculations. J. Chem. Theory. Comput., 3(3):1134-1142, 2007. (PDF)
    (** A "node patch" boundary element method --- the third low order BEM, mesh geometry correction, force calculation )
  86. B. Z. Lu, X. L. Cheng, J. F. Huang, and J. A. McCammon. Order N algorithm for computation of electrostatic interactions in biomolecular systems. Proc. Natl. Acad. Sci. U. S. A., 103(51):19314-19319, 2006. (PDF)
    ( * Fast multipole, well-conditioned boundary integral equations, multidomains )
  87. T. J. Hou, K. Chen, W. McLaughlin, B. Z. Lu, and W. Wang. Computational analysis and prediction of the Binding Motif and Protein Interacting Partners of the Abl SH3 domain. PLoS Computational Biology, 2(1):e1, 2006.
  88. T. J. Hou, W. McLaughlin, B. Z. Lu, K. Chen, and W. Wang. Prediction of Binding Affinities between the Human Amphiphysin-1 SH3 Domain and Its Peptide Ligands Using Homology Modeling, Molecular dynamics and Molecular Field Analysis. J. Proteome research, 5(1):32-43, 2006. (PDF)
  89. X. L. Cheng, B. Z. Lu, B. Grant, R. Law, and J. A. McCammon. Channel opening motion of \alpha 7 nicotinic acetylcholine receptor as suggested by normal mode analysis. J. Mol. Biol., 355(2):310-324, 2006. (PDF)
    ( * nAChR, normal model analysis, channel gating )
  90. M. U. Ung, B. Z. Lu*, and J. A. McCammon. E230Q mutation of the catalytic subunit of cAMP-dependent protein kinase affects local structure and the binding of peptide inhibitor. Biopolymers, 81(6):428-439, 2006. (PDF)
    ( * PKA, E230Q mutation effect, peptide binding )
  91. B. Z. Lu, X. L. Cheng, T. J. Hou, and J. A. McCammon. Calculation of the Maxwell stress tensor and the Poisson-Boltzmann force on a solvated molecular surface using hypersingular boundary integrals. J. Chem. Phys., 123(8):084904, 2005. (PDF)
    Also selected for the September 15, 2005 issue of Virtual Journal of Biological Physics Research. link
    ( * Maxwell stress tensor, strong singular and hypersingular integrals, BEM, PB force and torque )
  92. B. Z. Lu, D. Q. Zhang, and J. A. McCammon. Computation of electrostatic forces between solvated molecules determined by the Poisson-Boltzmann equation using a boundary element method. J. Chem. Phys., 122(21):214102, 2005. (PDF)
    Also selected for the June 1, 2005 issue of Virtual Journal of Biological Physics Research. link
    ( * A set of boundary integral equations derived from energy variation principle for calculations of the PB forces between biomolecules )
  93. B. Z. Lu, C. F. Wong, and J. A. McCammon. Release of ADP from the catalytic subunit of protein kinase A: A molecular dynamics simulation study. Protein Sci., 14(1):159-168, 2005. (PDF)
  94. B. Z. Lu and C. F. Wong. Direct calculation of entropy loss due to reduced translational and rotational motions upon molecular binding. Biopolymers, 79:277-285, 2005. (PDF)
    ( * Entropy calculation, formulations, entropy loss of bound water molecules and ATP )
  95. Y. H. Yu, B. Z. Lu*, J. G. Han, and P. F. Zhang. Scoring the protein-protein docked structures based on the balance and tightness of binding. J. Comput. Aided Mol. Des, 18(4):251-260, 2004.
  96. J. G. Han, Z. Y. Ren, and B. Z. Lu. Geometries and stabilities of re-doped si-n (n=1-12) clusters: a density functional investigation. J. Phys. Chem. A, 108(23):5100-5110, 2004.
  97. B. Z. Lu, B. H. Wang, W. Z. Chen, and C. X. Wang. A new computational approach for real protein folding prediction. Protein Eng., 16(9):659-663, 2003. (PDF)
    ( * Relative entropy, protein folding )
  98. Y. H. Yu, C. H. Li, B. Z. Lu, W. Z. Chen, and C. X. Wang. A new method to select the near-native conformations from the docked structures. Acta Phys.-Chim. Sin. (in Chinese), 19(8):757-761, 2003.
  99. B. Z. Lu, C. X. Wang, and B. H. Wang. A new minimization method for real protein folding prediction. Chin. J. Chem. Phys. (in Chinese), 16(2):117-121, 2003.
  100. W. Y. Wang, B. Z. Lu, W. Z. Chen, and C. X. Wang. Study on the stability of insulin hexamer in solution by molecular dynamics simulations. Acta Chim. Sin. (in Chinese), 60(12):2129-2134, 2002.
  101. W. Y. Wang, B. Z. Lu, W. Z. Chen, and C. X. Wang. The study on the flexibility of insulin hexamer in solution by molecular dynamics simulations. Acta Biophysica Sinica (in Chinese), (19):35-40, 2003.
  102. B. Z. Lu, W. Z. Chen, C. X. Wang, and X. J. Xu. Protein molecular dynamics with electrostatic force entirely determined by a single Poisson-Boltzmann calculation. Proteins, 48(3):497-504, 2002. (PDF)
    ( * Finite difference Poisson-Boltzmann molecular dynamics simulation )
  103. X. H. Ma, C. H. Li, B. Z. Lu, W. Z. Chen, C. X. Wang, and X. J. Xu. Salt and pH-dependent properties of native and mutant insulin. Chin. Sci. Bull., 47(6):464-466, 2002.
  104. B. Z. Lu, C. X. Wang, W. Z. Chen, S. Z. Wan, and Y. Y. Shi. A stochastic dynamics simulation study associated with hydration force and friction memory effect. J. Phys. Chem. B, 104(29):6877-6883, 2000. (PDF)
    ( * Generalized Langevin dynamics, friction memory, boundary element method Poisson-Boltzmann force )
  105. B. Z. Lu, W. Z. Chen, and C. X. Wang. The generalized Langevin dynamics associated with boundary element method. Chinese Science Bulletin, 45:1482-1486, 2000.

　

　

Others (published in my notebook, disappeared journal, or somewhere in an old mountain and forest you may not reach :) )

“量子原理与艺术哲学”（Quantum theory and the philosophy of art）, (in Chinese中文) 1999, (maybe printed in 2002). (PDF)
( * 艺术中的不确定性，及量化评价的可能性？ )

Ben-Zhuo Lu 2012-4-24