Journal Publications

1. Yuze Zhang, Xuelong Gu, Yushun Wang, Xianmin Xu*, Lei Zhang*. Solution landscape of droplet on rough surfaces: wetting transition and directional transport, arXiv:2410.04829. [Link].
   
   
2. Shuonan Wu, Bing Yu, Yuhai Tu*, Lei Zhang*. Solution landscape of reaction-diffusion systems reveals a nonlinear mechanism and spatial robustness of pattern formation, arXiv:2408.10095. [Link].
   
   
3. Baoming Shi, Yucen Han, Chengdi Ma, Apala Majumdar, Lei Zhang. A Modified Landau-de Gennes Theory for Smectic Liquid Crystals: Phase Transitions and Structural Transitions, arXiv:2408.03343. [Link]
   
   
4. Yucen Han, Apala Majumdar, Baoming Shi, Dawei Wu, Lei Zhang*, Pingwen Zhang. A diffuse-interface Landau-de Gennes model for free-boundary problems in the theory of nematic liquid crystals, arXiv:2407.21437. [Link]
   
   
5. Lei Zhang, Pingwen Zhang, Xiangcheng Zheng*. Exponential Lyapunov stability of high-index saddle dynamics with or without acceleration, submitted.
   
   
6. Tunan Kao, He Zhang, Lei Zhang, Jin Zhao. pETNNs: Partial Evolutionary Tensor Neural Networks for Solving Time-dependent Partial Differential Equations, arXiv:2403.06084. [Link]
   
   
7. Shuai Miao, Ziqi Liu, Lei Zhang, Pingwen Zhang, Xiangcheng Zheng. Construction and analysis for Adams explicit discretization of high-index saddle dynamics, submitted.
   
   
8. Miao Huang, Junda Ying, Yuxuan Wang, Haijun Zhou, Lei Zhang*, Weikang Wang*. Geometric Quantification of Cell Phenotype Transition Manifolds with Information Geometry, bioRxiv, 2023-12. [Link]
   
   
9. Yue Luo, Lei Zhang, Xiangcheng Zheng. Accelerated high-index saddle dynamics method for searching high-index saddle points, arXiv:2310.04656. [Link]
   
   
10. Lei Zhang, Pingwen Zhang, Xiangcheng Zheng. Understanding high-index saddle dynamics via numerical analysis, accepted by Comm Math Sci.. [Link]
    
    
11. Shun Wang, Tengfei Wang, Shuonan Wu, Lei Zhang, Xiufen Zou. Uncovering the Impact of Ecological Interactions on Cancer Progression through Mathematical Modeling and Solution Landscape, accepted by SIAM J. Appl. Math..
    
    
12. Tiejun Zhou, Lei Zhang, Pingwen Zhang, An-Chang Shi, Kai Jiang*. Nucleation and phase transition of decagonal quasicrystals, J. Chem. Phys., 161, 164503 (2024).[Link]
    
    
13. Lu Li, Bing Yu, Pengyue Gao, Jian Lv*, Lei Zhang*, Yanchao Wang*, Yanming Ma*. Representing crystal potential energy surfaces via a stationary-point network, Acta Materialia, 281, 120403 (2024).[Link]
    
    
14. Bin Du, He Zhang, Xiangle Cheng, Lei Zhang. Neural Quantile Optimization for Edge-Cloud Computing, Computer Networks, 253, 110713 (2024). [Link]
    
    
15. Qirui Guo, Musu Yuan, Lei Zhang*, Minghua Deng*. scPLAN: A hierarchical computational framework for single transcriptomics data annotation, integration and cell-type label refinement, Briefings in Bioinformatics, 25.4 (2024). [Link]
    
    
16. Yue Luo, Lei Zhang, Pingwen Zhang, Zhiyi Zhang, Xiangcheng Zheng. Semi-implicit method of high-index saddle dynamics and application to construct solution landscape, Numerical Methods for Partial Differential Equations, e23123 (2024). [Link]
    
    
17. Baoming Shi, Yucen Han, Apala Majumdar, Lei Zhang. Multistability for Nematic Liquid Crystals in Cuboids with Degenerate Planar Boundary Conditions, SIAM J. Appl. Math., 84 (2), 756-781 (2024). [Link]
    
    
18. Lei Zhang, Pingwen Zhang, Xiangcheng Zheng*. Probabilistic Error Estimate for Numerical Discretization of High-Index Saddle Dynamics with Inaccurate Models, Ann. Appl. Math., 40(1), 1-20 (2024). [Link]
    
    
19. Jianyuan Yin, Zhen Huang, Yongyong Cai, Qiang Du, Lei Zhang*. Revealing Excited States of Rotational Bose-Einstein Condensates, The Innovation, 5(1), 100546 (2024). [Link]
    
    
20. Yucen Han, Baoming Shi, Lei Zhang, Apala Majumdar. A Reduced Landau-de Gennes Study for Nematic Equilibria in Three-Dimensional Prisms, IMA Journal of Applied Mathematics, hxad031 (2023). [Link]
    
    
21. Gang Xue, Xiaoyi Zhang, Wanqi Li, Lu Zhang, Zongxu Zhang, Xiaolin Zhou, Di Zhang, Lei Zhang*, Zhiyuan Li*. A Logic-incorporated Gene Regulatory Network Deciphers Principles in Cell Fate Decisions, eLife 12:RP88742 (2023). [Link]
    
    
22. Lei Zhang, Pingwen Zhang, Xiangcheng Zheng. Error estimate for semi-implicit method of sphere-constrained high-index saddle dynamics, Chinese Annals of Mathematics, Series B, 44(5), 765–780 (2023). [Link]
    
    
23. Lei Zhang. Construction of solution landscapes for complex systems, Mathematica Numerica Sinica, 45(3), 267-283 (2023). [Link]
    
    
24. Lei Zhang*, Pingwen Zhang, Xiangcheng Zheng. A model-free shrinking-dimer saddle dynamics for finding saddle point and solution landscape, Japan Journal of Industrial and Applied Mathematics (2023). [Link]
    
    
25. Donghang Zhang, Lei Zhang*. Spectral Deferred Correction Method for Landau-Brazovskii Model with Convex Splitting Technique, Journal of Computational Physics, 491 (2023) 112348. [Link]
    
    
26. Lei Zhang, Pingwen Zhang, Xiangcheng Zheng*. Discretization and index-robust error analysis for constrained high-index saddle dynamics on high-dimensional sphere, Science China Mathematics (2023). [Link]
    
    
27. Baoming Shi, Yucen Han, Jianyuan Yin, Apala Majumdar, Lei Zhang*. Hierarchies of Critical Points of a Landau-de Gennes Free Energy on Three-Dimensional Cuboids, Nonlinearity, 36, 2631 (2023). [Link]
    
    
28. Yuze Zhang, Xuguang Yang, Lei Zhang, Yiteng Li, Tao Zhang, Shuyu Sun*. Energy landscape analysis for two-phase multi-component NVT flash systems by using ETD type high-index saddle dynamics, Journal of Computational Physics, 477, 111916 (2023).
    
    
29. Xiangyu Kuang, Guoye Guan, Chao Tang*, Lei Zhang*. MorphoSim: An efficient and scalable phase-field framework for accurately simulating multicellular morphologies, npj Systems Biology and Applications, (2023) 9:6. [Link]
    
    
30. Guoye Guan, Xiangyu Kuang, Chao Tang*, Lei Zhang*. Comparison between phase-field model and coarse-grained model for characterizing cell-resolved morphological and mechanical properties in a multicellular system, Communications in Nonlinear Science and Numerical Simulation, 117, 106966 (2023).[Link]
    
    
31. Lei Zhang, Pingwen Zhang, Xiangcheng Zheng. Mathematical and numerical analysis to shrinking-dimer saddle dynamics with local Lipschitz conditions, CSIAM Trans. Appl. Math., 4(1), 157-176 (2023).[Link]
    
    
32. Lei Zhang, Pingwen Zhang, Xiangcheng Zheng. Error estimates for Euler discretization of high-index saddle dynamics, SIAM Journal on Numerical Analysis, 60(5), 2925-2944 (2022). [Link]
    
    
33. Yue Luo, Xiangcheng Zheng, Xiangle Cheng, Lei Zhang. Convergence analysis of discrete high-index saddle dynamics, SIAM Journal on Numerical Analysis, 60(5), 2731-2750 (2022). [Link]
    
    
34. Baoming Shi, Yucen Han, Lei Zhang. Nematic liquid crystals in a rectangular confinement: solution landscape and bifurcation, SIAM J. Appl. Math.82(5), 1808-1828 (2022). [Link]
    
    
35. Lingxia Qiao, Zhi-Bo Zhang, Wei Zhao, Ping Wei*, Lei Zhang*. Network design principle for robust oscillatory behaviors with respect to biological noise, eLife, 11:e76188 (2022). [Link]
    
    
36. Xiaomei Yao, Jie Xu, Lei Zhang*. Transition pathways in Cylinder-Gyroid interface, Commun. Comput. Phys., 32, 810-828 (2022). [Link]
    
    
37. Bing Yu, Xiangcheng Zheng, Pingwen Zhang, Lei Zhang*. Computing solution landscape of nonlinear space-fractional problems via fast approximation algorithm, Journal of Computational Physics, 468, 111513 (2022). [Link]
    
    
38. Chunmei Guan, Lingxia Qiao, Yuanyuan Xiong, Lei Zhang*, Yuling Jiao*. Coactivation of antagonistic genes stabilizes polarity patterning during shoot organogenesis, Science Advances, 8, eabn0368 (2022). [Link]
    
    
39. Yucen Han, Joseph Harris, Apala Majumdar, Lei Zhang. Elastic anisotropy in the reduced Landau-de Gennes model for square domains, Proceedings of the Royal Society A, 478:20210966 (2022). [Link]
    
    
40. Xiaolu Guo, Tao Tang, Minxuan Duan, Lei Zhang*, Hao Ge*. The nonequilibrium mechanism of noise-enhanced drug synergy in HIV latency reactivation, iScience, 25, 104358 (2022). [Link]
    
    
41. Xiaomei Yao, Lei Zhang*, Jeff Z.Y. Chen*. Defect patterns of two-dimensional nematic liquid crystals in confinement, Physical Review E, 105, 044704 (2022). [Link]
    
    
42. Jianyuan Yin, Zhen Huang, Lei Zhang*. Constrained high-index saddle dynamics for the solution landscape with equality constraints, Journal of Scientific Computing, 91:62 (2022). [Link]
    
    
43. Xiangyu Kuang, Guoye Guan, Ming-Kin Wong, Lu-Yan Chan, Zhongying Zhao, Chao Tang*, Lei Zhang*. Computable early Caenorhabditis elegans embryo with a phase field model, PLOS Computational Biology 18(1): e1009755 (2022). [Link]
    
    
44. Jianyuan Yin, Lei Zhang*, Pingwen Zhang. Solution Landscape of the Onsager Model Identifies Non-axisymmetric Critical Points. Physica D: Nonlinear Phenomena,430, 133081 (2022). [Link]
    
    
45. Jianyuan Yin, Kai Jiang, An-Chang Shi*, Pingwen Zhang*, Lei Zhang*. Transition pathways connecting crystals and quasicrystals, Proceedings of the National Academy of Sciences, 118 (49), e2106230118 (2021). [Link][Code]
    
    
46. Yuze Zhang, Yiteng Li, Lei Zhang, Shuyu Sun*. Construction of a Minimum Energy Path for the VT Flash Model by the String Method Coupled with the Exponential Time Differencing Scheme, Commun. Comput. Phys., 30, 1529-1544 (2021). [Link]
    
    
47. Yucen Han, Jianyuan Yin, Yucheng Hu, Apala Majumdar, Lei Zhang*. Solution Landscapes of the Simplified Ericksen-Leslie Model and its Comparison with the Reduced Landau-de Gennes Model, Proceedings of the Royal Society A, 477:20210458 (2021). [Link].
    
    
48. Wei Wang, Lei Zhang, Pingwen Zhang. Modeling and Computation of Liquid Crystals, Acta Numerica, 30, 765-851 (2021). [Link]
    
    
49. Zhen Xu, Yucen Han, Jianyuan Yin, Bing Yu, Yasumasa Nishiura*, Lei Zhang*. Solution landscapes of the diblock copolymer-homopolymer model under two-dimensional confinement, Physical Review E, 104, 014505 (2021). [Link]
    
    
50. Wei Zhao, Lingxia Qiao, Shiyu Yan, Qing Nie*, Lei Zhang*. Modeling of histone modifications reveals formation mechanism and function of bivalent chromatin, iScience, 24, 102732 (2021). [Link][Code]
    
    
51. Yuanyuan Xiong, Binbin Wu, Fei Du, Xiaolu Guo, Caihuan Tian, Jinrong Hu, Shouqin Lu, Mian Long, Lei Zhang*, Ying Wang*, Yuling Jiao*. A crosstalk between auxin and brassinosteroid regulates leaf shape by modulating growth anisotropy, Molecular Plant, 14, 949–962 (2021). [Link]
    
    
52. Yucen Han, Jianyuan Yin, Pingwen Zhang, Apala Majumdar, Lei Zhang*. Solution landscape of a reduced Landau--de Gennes model on a hexagon, Nonlinearity, 34, 2048-2069 (2021). [Link]
    
    
53. Ruotai Li, Qiang Du, Lei Zhang*. Numerical discretization of variational phase field model for phase transitions in ferroelectric thin films, Commun. Comput. Phys., 29, 729-746 (2021). [Link]
    
    
54. Bing Yu, Lei Zhang*. Global optimization-based dimer method for finding saddle points, Discrete Contin. Dyn. Syst. Ser. B 26(1): 741-753 (2021). [Link]
    
    
55. Jianyuan Yin, Bing Yu, Lei Zhang*. Searching the solution landscape by generalized high-index saddle dynamics, Sci. China Math. 64, 1801–1816 (2021). [Link]
    
    
56. Kuan Tao, Jin Wang, Xiangyu Kuang, Weikang Wang, Feng Liu*, Lei Zhang*. Tuning cell motility via cell tension with a mechanochemical cell migration model, Biophysical Journal, 118, 2894–2904 (2020). [Link]
    
    
57. Yucen Han, Apala Majumdar, Lei Zhang. A Reduced Study for Nematic Equilibria on Two-Dimensional Polygons, SIAM J. Appl. Math., 80(4), 1678–1703 (2020). [Link]
    
    
58. Qiang Du, Ruotai Li, Lei Zhang. Variational Phase Field Formulations of Polarization and Phase Transition in Ferroelectric Thin Films, SIAM J. Appl. Math., 80(3), 1590–1606 (2020). [Link]
    
    
59. Jianyuan Yin, Yiwei Wang, Jeff Z.Y. Chen*, Pingwen Zhang*, Lei Zhang*. Construction of a pathway map on a complicated energy landscape, Physical Review Letters 124, 090601 (2020). [Link]
    
    
60. Qing Nie*, Lingxia Qiao, Yuchi Qiu, Lei Zhang*, Wei Zhao. Noise control and utility: from gene regulatory network to spatial patterning, Sci. China Math 63, 425–440 (2020). [Link]
    
    
61. Yucen Han, Zirui Xu, An-Chang Shi*,Lei Zhang*. Pathways connecting two opposed bilayers with a fusion pore: A molecularly-informed phase field approach, Soft Matter, 2020, 16, 366-374. [Link]
    
    
62. Jianyuan Yin, Lei Zhang. Pingwen Zhang, High-index Optimization-based Shrinking Dimer Method for Finding High-Index Saddle Points, SIAM Journal on Scientific Computing, 41 (6), A3576-A3595. 2019.[Link]
    
    
63. Lingxia Qiao, Wei Zhao, Chao Tang*, Qing Nie*, Lei Zhang*. Network Topologies That Can Achieve Dual Function of Adaptation and Noise Attenuation, Cell Systems 9, 1–15, 2019.[Link]
    
    
64. Yucen Han, Yucheng Hu*, Pingwen Zhang*, Lei Zhang*. Transition Pathways between Defect Patterns in Confined Nematic Liquid Crystals, J. Comput. Phys. 396 (2019) 1–11.[Link]
    
    
65. Chunhe Li*, Lei Zhang*,Qing Nie*, Landscape reveals critical network structures for sharpening gene expression boundaries, BMC Systems Biology 12:67, 2018. [Link]
    
    
66. Lina Meinecke, Praveer Sharma, Huijing Du, Lei Zhang, Qing Nie*, Thomas Schilling*. Modeling craniofacial development reveals spatiotemporal constraints on robust patterning of the mandibular arch, PLoS Comput Biol 14(11): e1006569, 2018. [Link]
    
    
67. Boyan Li, Lei Zhang*, Chengliang Li, Qiulin Li, Jun Chen, Guogang Shu, Yuqing Weng, Ben Xu, Shenyang Hu*, Wei Liu*. Phase Field Simulation of Critical Nuclei and Minimum Energy Paths of Cu/Mn/Ni Precipitates in Fe-Cu-Mn (Ni) Alloys, Journal of Nuclear Materials 507, 59-67, 2018. [Link]
    
    
68. Peijia Yu, Qing Nie*, Chao Tang*, Lei Zhang*. Nanog induced intermediate state in regulating stem cell differentiation and reprogramming, BMC Systems Biology 12:22, 2018. [Link]
    
    
69. Bihai Shi, Xiaolu Guo, Ying Wang, Yuanyuan Xiong, Jin Wang, Ken-ichiro Hayashi, Jinzhi Lei, Lei Zhang*, Yuling Jiao*. Feedback from Lateral Organs Controls Shoot Apical Meristem Growth by Modulating Auxin Transport, Developmental Cell, 44, 204-216, 2018. [Link]
    
    
70. Boyan Li, Lei Zhang*, Chengliang Li, Shenyang Hu, Qiulin Li, Jun Chen, Guogang Shu, Yuqing Weng, Ben Xu*, Wei Liu*. Finding Non-Classical Critical Nuclei and Minimum Energy Path of Cu Precipitates in Fe-Cu Alloys, Modelling Simul. Mater. Sci. Eng. 25 085006, 2017. [pdf]
    
    
71. Yanru An, Guosheng Xue, Xiaowei Zhou, Weichuan Yu, Toyotaka Ishibashi, Lei Zhang*, Yan Yan*. Apical constriction is driven by a pulsatile apical myosin network in delaminating Drosophila neuroblasts, Development, 144, 2153-2164, 2017. [Link]
    
    
72. Weikang Wang, Kuan Tao, Jin Wang, Gen Yang, Qi Ouyang, Yugang Wang, Lei Zhang*, Feng Liu*. Exploring the inhibition effect of membrane tension on cell polarization, PLoS Comput Biol 13(1): e1005354. doi:10.1371/ journal.pcbi.1005354, 2017. [Link]
    
    
73. Lei Zhang, Weiqing Ren, Amit Samanta, Qiang Du*. Recent Developments in Computational Modeling of Nucleation in Phase Transformations, npj Computational Materials (2016) 2, 16003. [pdf]
    
    
74. Lei Zhang, Qiang Du, Zhenzhen Zheng. Optimization-based Shrinking Dimer Method for Finding Transition States, SIAM Journal on Scientific Computing 38:1, A528-A544, 2016. [pdf]
    
    
75. Amanda Cinquin, Likun Zheng, Harry P. Taylor, Adrian Paz, Lei Zhang, Michael Chiang, Josh Snow, Qing Nie, Olivier Cinquin*. Semi-permeable Diffusion Barriers Enhance Patterning Robustness in the C. elegans Germline, Developmental Cell 35, 405-417, 2015. [pdf]
    
    
76. Tian Hong, Ernest S. Fung, Lei Zhang, Edwin S. Monuki*, Qing Nie*. Semi-adaptive response and noise attenuation in bone morphogenetic protein signalling, J. R. Soc. Interface 12: 20150258, 2015.[pdf]
    
    
77. Lei Zhang, Jingyan Zhang, Qiang Du*. Finding Critical Nuclei in Phase Transformations by Shrinking Dimer Dynamics and its Variants, Commun. Comput. Phys., 16, pp. 781-798, 2014. [pdf]
    
    
78. Yulan Li*, Shenyang Hu, Lei Zhang, Xin Sun. Non-classical nuclei and growth kinetics of Cr precipitates in FeCr alloys during aging, Modelling Simul. Mater. Sci. Eng., 22, 025002, 2014. [pdf]
    
    
79. Dongyong Wang, Lei Zhang, Qing Nie*. Array-representation Integration Factor Method for High-dimensional Systems, J. Comput. Phys., 258, 585-600, 2014. [pdf]
    
    
80. Lei Zhang, Kelly Radtke, Likun Zheng, Anna Cai, Tom Schilling*, Qing Nie*. Noise Drives Sharpening of Gene Expression Boundaries in the Zebrafish Hindbrain, Molecular Systems Biology 8:613, 2012. [pdf]
    
    
81. Lei Zhang, Arthur Lander, Qing Nie*. A Reaction-Diffusion Mechanism Influences Cell Lineage Progression as a Basis for Formation, Regeneration, and Stability of Intestinal Crypts, BMC Systems Biology 6:93, 2012. [pdf]
    
    
82. Lei Zhang, Long-qing Chen, Qiang Du*. Simultaneous Prediction of Morphologies of a Critical Nucleus and an Equilibrium Precipitate in Solids, Commun. Comput. Phys., 7, 674-682, 2010. [pdf]
    
    
83. Tae Wook Heo*, Lei Zhang, Qiang Du, and Long-Qing Chen. Incorporating Non-classical Nuclei in Phase-field Simulations, Scripta Materialia, 63, 8-11, 2010. [pdf]
    
    
84. Lei Zhang*, Long-qing Chen, Qiang Du. Diffuse-Interface Approach to Predicting Morphologies of Critical Nucleus and Equilibrium Structure for Cubic to Tetragonal Transformations, J. Comput. Phys., 229, 6574-6584, 2010. [pdf]
    
    
85. Qiang Du, Lei Zhang. A constrained string method and its numerical analysis, Commun. Math. Sci., 7, 1039-1051, 2009. [pdf]
    
    
86. Lei Zhang, Long-qing Chen, Qiang Du*. Mathematical and Numerical Aspects of Phase-field Approach to Critical Morphology in Solids, Journal of Scientific Computing, 37, 89-102, 2008. [pdf]
    
    
87. Lei Zhang, Long-qing Chen, Qiang Du*. Diffuse-Interface Description of Strain-Dominated Morphology of Critical Nuclei in Phase Transformations, Acta Materialia, 56, 3568-3576, 2008. [pdf]
    
    
88. Lei Zhang*, Long-qing Chen*, Qiang Du*. Morphology of critical nuclei in solid state phase transformations, Physical Review Letters, 98, No.25, 265703, 2007. [pdf]

Conference Publications and Monograph

1. Lei Zhang, Long-qing Chen, Qiang Du. Phase-field Prediction of Critical Nucleus Morphology in Solids", Proceeding of the Fourth International Conference on Multiscale Materials Modeling, Tallahassee, FL, pp. 514-517, October 2008. [pdf]