个人简介
课题组新闻动态
2023/4, 祝贺殷鉴远和俞炳发表在SCIENCE CHINA Mathematics的文章“Yin J Y, Yu B, Zhang L. Searching the solution landscape by generalized high-index saddle dynamics. Sci China Math, 2021, 64: 1801–1816”获评第6届“SCIENCE CHINA Mathematics优秀论文奖”。
2023/4, 祝贺郑祥成的文章“Discretization and index-robust error analysis for constrained high-index saddle dynamics on high-dimensional sphere”被SCIENCE CHINA Mathematics顺利接受。此项工作与张平文院士合作完成。
2023/03, 祝贺石宝明和韩雨岑的文章“Hierarchies of Critical Points of a Landau-de Gennes Free Energy on Three-Dimensional Cuboids”被Nonlinearity顺利接受。此项工作与英国Strathclyde大学Apala Majumdar教授合作完成。
2023/01, 祝贺匡翔宇与关国业合作的文章“MorphoSim: An efficient and scalable phase-field framework for accurately simulating multicellular morphologies”被npj Systems Biology and Applications顺利接受，我们在此工作基础上开发了MorphoSim软件，并申请了相应的技术专利，该项工作与汤超院士合作完成。
2022/10, 祝贺匡翔宇与关国业合作的文章“Comparison between phase-field model and coarse-grained model for characterizing cell-resolved morphological and mechanical properties in a multicellular system”被Communications in Nonlinear Science and Numerical Simulation顺利接受，该项工作与汤超院士合作完成。
2022/9, 祝贺乔灵霞博士在《eLife》发表论文“Network design principle for robust oscillatory behaviors with respect to biological noise”。作为生命体的内在时钟，生物震荡的精确性对于信号转导、基因调控以及细胞周期等生命过程至关重要。然而在存在环境和自身噪声的情况下，生物网络如何实现精确振荡还尚不明确。本研究提出了振荡-抗噪双功能生物网络的设计原理，鉴定出带有自激活的抑制振荡子为稳健实现精确振荡的网络拓扑，揭示了长周期和高振幅分别作为衰减外源性噪声和内源性噪声的机制，有助于理解生命系统如何在噪声存在的情况下实现精确振荡，并且为人工合成精确振荡的网络提供了理论依据。此项工作与中国科学院合成所魏平研究员合作完成。
2022/8, 祝贺罗月和郑祥成的文章“Convergence analysis of discrete high-index saddle dynamics”被SIAM Journal on Numerical Analysis顺利接受。
2022/7, 祝贺俞炳和郑祥成的文章“Computing solution landscape of nonlinear space-fractional problems via fast approximation algorithm”被Journal of Computational Physics顺利接受。此项工作与张平文院士合作完成。
2022/7, 祝贺郑祥成的文章“Mathematical and numerical analysis to shrinking-dimer saddle dynamics with local Lipschitz conditions”被CSIAM Transactions on Applied Mathematics顺利接受。此项工作与张平文院士合作完成。
2022/7, 祝贺郑祥成的文章“Error estimates for Euler discretization of high-index saddle dynamics”被SIAM Journal on Numerical Analysis顺利接受。此项工作与张平文院士合作完成。
2022/6, 祝贺石宝明和韩雨岑的文章“Nematic liquid crystals in a rectangular confinement: solution landscape and bifurcation”被SIAM J. Appl. Math顺利接受。
2022/6, 祝贺乔灵霞博士在《Science Advances》发表论文“Coactivation of antagonistic genes stabilizes polarity patterning during shoot organogenesis"。器官形态建成过程中经常需要维持相互拮抗的基因同时表达，相邻分布的基因之间经常存在相互抑制的拮抗作用，维持二者表达区域的互斥。二者又需要共同存在，不能由一方完全抑制对方。本研究提出了一个“跷跷板” 模型—生长素信号同时激活 REV和 KAN1的表达以稳定维持两个区域的共存，从而在理论上可以维持发育斑图。此项工作与北大生命科学学院焦雨铃教授合作完成。《北大新闻网》
2022/4, 祝贺郭晓露的文章“The Nonequilibrium Mechanism of Noise Enhancer synergizing with Activator in HIV Latency Reactivation"被iScience顺利接受。此项工作与北大北京国际数学研究中心葛颢教授合作完成。
2022/4, 祝贺韩雨岑博士的文章“Elastic anisotropy in the reduced Landau-de Gennes model"被Proceedings of the Royal Society A顺利接受。此项工作与英国Strathclyde大学Apala Majumdar教授合作完成。
2022/4, 祝贺姚小妹的文章“Transition pathways in Cylinder-Gyroid interface"被Commun. Comput. Phys.顺利接受。此项工作与中科院计算数学所徐劼研究员合作完成。
2022/3, 祝贺姚小妹的文章“Defect patterns of two-dimensional nematic liquid crystals in confinement"被Physical Review E顺利接受。此项工作与加拿大Waterloo大学陈征宇教授合作完成。
2022/3, 祝贺殷鉴远和黄桢的文章“Constrained high-index saddle dynamics for the solution landscape with equality constraints"被Journal of Scientific Computing顺利接受。我们在原有的鞍点动力学基础上发展了受限鞍点动力学，从而构建带约束的能量景观。
2022/01, 祝贺匡翔宇在《PLOS Computational Biology》发表论文“Computable early Caenorhabditis elegans embryo with a phase field model"。细胞是生命的最小活动单位。不同物种、器官、组织的细胞具有不同的形态，而形态表征了细胞的力学属性和功能。什么样的数学物理方程能够准确描述细胞形态的动力学特征，对于生物力学、细胞生物学和发育生物学都是一个重要问题。秀丽隐杆线虫（Caenorhabditis elegans）拥有单细胞的发育精度，即每个细胞的分裂时间、分裂方向、运动路径、命运身份等属性在不同个体间保持高度一致。我们的工作利用线虫胚胎形态数据构建了一个相场模型，可以准确计算真实胚胎的形态变化并且反推底层的细胞力学属性，并利用该模型解析线虫胚胎的早期发育过程。此项工作与汤超院士合作完成。《BICMR News》
2021/12, 祝贺殷鉴远博士在《PNAS》发表论文“Transition pathways connecting crystals and quasicrystals"。自1984年准晶被发现以来，尽管人们对准晶的研究已取得了巨大的成就，但准晶的成核问题，即如何从晶体中涌现出准晶，仍然是凝聚态物理学中一个长久以来尚未解决的问题。这里的困难主要来自于准晶和晶体结构是非公度的，因此它们之间没有明显的外延关系。我们将发展的鞍点动力学应用到Landau相变理论来探求准晶的成核。通过计算Lifshitz-Petrich 模型，我们获得了连接6方晶体和12转准晶的精确临界核和相变转移路径，发现了晶体和准晶相之间的相变可以遵循两种可能的路径，分别对应于单步相变和“晶体-层状准晶-准晶”的两步相变。此项工作与张平文院士、加拿大McMaster大学史安昌教授、湘潭大学蒋凯教授合作完成。《北大新闻网》
2021/11, 祝贺殷鉴远博士在《Physica D: Nonlinear Phenomena》发表论文“Solution Landscape of the Onsager Model Identifies Non-axisymmetric Critical Points"。该论文从计算上回答了之前液晶Onsager模型的一些公开问题，验证了极小解的轴对称性，找出了一系列Onsager模型的非轴对称解，以及完整刻画了Onsager模型的解景观。此项工作与张平文院士合作完成。
2021/09, 欢迎张鹤博士加入我们课题组！张鹤博士毕业于美国宾州州立大学。
2021/8, 祝贺张雨泽博士的文章“Construction of a minimum energy path for the VT flash model by the string method coupled with the exponential time differencing scheme"被Commun. Comput. Phys.顺利接受。此项工作与沙特阿拉伯阿卜杜拉国王科技大学(KAUST)孙树瑜教授合作完成。
2020/08, 我们与张平文院士、王伟研究员合作在《Acta Numerica》发表综述论文“Modelling and Computation of Liquid Crystals”。液晶是一种介于液体和晶体之间的软物质，具有广泛的工业应用价值。论文首先介绍了液晶分子三类不同层次的数学模型：分子模型、张量模型和向量模型，及其相互联系；接下来介绍了计算液晶稳态缺陷和流体动力学模型的数值方法以及近年来提出的解景观方法；论文最后给出了总结并提出了一些新的展望。《北大新闻网》
2021/8, 祝贺韩雨岑博士和殷鉴远博士的文章“Solution Landscapes of the Simplified Ericksen-Leslie Model and its Comparison with the Reduced Landau-de Gennes Model"被Proceedings of the Royal Society A顺利接受。此项工作与英国Strathclyde大学Apala Majumdar教授和首师大胡煜成教授合作完成。
2021/6, 祝贺徐真博士的文章“Solution landscapes of the diblock copolymer-homopolymer model under two-dimensional confinement"被Physical Review E顺利接受。此项工作与Hokkaido University的Yasumasa Nishiura教授合作完成。
2021/6, 祝贺赵伟博士的文章“Modeling of histone modifications reveals formation mechanism and function of bivalent chromatin"被iScience顺利接受。此项工作与UC Irvine大学聂青教授合作完成。
2021/06, 热烈祝贺殷鉴远、李若泰同学顺利通过博士论文答辩，闫诗宇、谢地同学顺利通过硕士论文答辩！
2020/10, 祝贺韩雨岑和殷鉴远的文章“Solution landscape of a reduced Landau-de Gennes model on a hexagon"被Nonlinearity顺利接受。此项工作与张平文院士、英国Strathclyde大学Apala Majumdar教授合作完成。
2020/10, 热烈祝贺课题组17本王浩然、黄桢在2020丘成桐大学生数学竞赛上取得佳绩！王浩然1金（个人全能）2银（应用与计算数学、分析与微分方程），黄桢1铜（应用与计算数学）[Link]。
2020/10, 欢迎姚小妹博士加入我们课题组！姚小妹博士毕业于北京师范大学。
2020/09, 热烈祝贺韩雨岑博士获得英国皇家学会“Newton International Fellowship"，她将与英国Strathclyde大学Apala Majumdar教授一起合作研究。
2020/08, 祝贺李若泰的文章“Numerical discretization of variational phase field model for phase transitions in ferroelectric thin films"被Commun. Comput. Phys.顺利接受。此项工作与哥伦比亚大学杜强教授合作完成。
2020/07, 欢迎张东航博士加入我们课题组！张东航博士毕业于中科院数学与系统科学研究院。
2020/07, 祝贺俞炳和殷鉴远合作的文章“Searching the solution landscape by generalized high-index saddle dynamics"被SCIENCE CHINA Mathematics顺利接受。我们提出了普适的高阶鞍点动力学方法来构建解景观。
2020/06, 热烈祝贺乔灵霞、郭晓露、韩雨岑、赵伟四位同学顺利通过博士论文答辩！他们将分别在UCSD，UCLA，U. of Strathclyde, UCI做博士后。
2020/04, 祝贺陶宽的文章“Tuning cell motility via cell tension with a mechanochemical cell migration model”被Biophysical Journal接受。此项工作与北大定量生物学中心刘峰课题组合作完成。
2020/04, 祝贺李若泰的文章“Variational Phase Field Formulations of Polarization and Phase Transition in Ferroelectric Thin Films”被SIAM Journal on Applied Mathematics接受。此项工作与哥伦比亚大学杜强教授合作完成。
2020/04, 祝贺韩雨岑的文章“A Reduced Study for Nematic Equilibria on Two-Dimensional Polygons”被SIAM Journal on Applied Mathematics接受。此项工作与英国Strathclyde大学Apala Majumdar教授合作完成。
2020/03, 祝贺俞炳的文章“Global optimization-based dimer method for finding saddle points”被Discrete Contin. Dyn. Syst. Ser. B接受。
2020/03, 祝贺殷鉴远在《Phys. Rev. Lett.》发表论文“Construction of a pathway map on a complicated energy landscape”。该论文发展了一种在复杂能量景观上构建“路径图”的计算方法，为解决多解问题提供了一个高效的工具。此项工作与张平文院士、加拿大滑铁卢大学陈征宇教授合作完成。《北大新闻网》。
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Journal Publications
Yucen Han, Jianyuan Yin, Pingwen Zhang, Apala Majumdar, Lei Zhang. Solution landscape of a reduced Landau--de Gennes model on a hexagon, arXiv:2003.07643. [Link]
Ruotai Li, Qiang Du, Lei Zhang. Efficient Variational Phase Field Method for Phase Transitions in Ferroelectric Thin Films, arXiv:2003.00416. [Link]
Jianyuan Yin, Bing Yu, Lei Zhang. Searching the solution landscape by generalized high-index saddle dynamics, arXiv:2002.10690. [Link]
Xiaolu Guo, Tao Tang, Minxuan Duan, Lei Zhang, Hao Ge. The Nonequilibrium Mechanism of Noise Enhancer synergizing with Activator in HIV Latency Reactivation, bioRxiv 2020.01.14.905653. [Link]
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, accepted. [Link]
Yucen Han, Apala Majumdar, Lei Zhang. A Reduced Study for Nematic Equilibria on Two-Dimensional Polygons, SIAM Journal on Applied Mathematics, accepted. [Link]
Qiang Du, Ruotai Li, Lei Zhang. Variational Phase Field Formulations of Polarization and Phase Transition in Ferroelectric Thin Films, SIAM Journal on Applied Mathematics, accepted. [Link]
Bing Yu, Lei Zhang. Global optimization-based dimer method for finding saddle points, Discrete Contin. Dyn. Syst. Ser. B (2020), doi: 10.3934/dcdsb.2020139. [Link]
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]
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]
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]
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]
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]
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]
Chunhe Li, Lei Zhang,Qing Nie, Landscape reveals the underlying mechanisms for sharpening the gene expression boundaries, BMC Systems Biology 12:67, 2018. [Link]
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]
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]
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]
Bihai Shi, Xiaolu Guo, Ying 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]
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.
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]
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]
Lei Zhang, Weiqing Ren, Amit Samanta, Qiang Du. Recent Developments in Computational Modeling of Nucleation in Phase Transformations, npj Computational Materials (2016) 2, 16003.
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.
Amanda Cinquin, Likun Zheng, Harry P. Taylor, Adrian Paz, Lei Zhang, Michael Chiang, Josh Snow, Qing Nie, Olivier Cinquin. Semi-permeable diffusion barriers provide patterning robustness against spatial noise in morphogen release, Developmental Cell 35, 405-417, 2015.
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.
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.
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.
Dongyong Wang, Lei Zhang, Qing Nie. Array-representation Integration Factor Method for High-dimensional Systems, J. Comput. Phys., 258, 585-600, 2014.
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.
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.
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.
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.
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.
Qiang Du, Lei Zhang. A constrained string method and its numerical analysis, Commun. Math. Sci., 7, 1039-1051, 2009.
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.
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.
Lei Zhang, Long-qing Chen, Qiang Du. Morphology of critical nuclei in solid state phase transformations, Physical Review Letters, 98, No.25, 265703, 2007.
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