博士 数学科学学院, 1992
北京大学
学士 数学科学学院, 1988
北京大学
Interparticle interactions with multiple length scales play a pivotal role in the formation and stability of quasicrystals. Choosing a minimal set of length scales to stabilize a given quasicrystal is a challenging problem. To address this challenge, we propose a symmetry-preserving screening method (SPSM) to design a Landau theory with a minimal number of length scales-referred to as the minimal Landau theory-that includes only the essential length scales necessary to stabilize quasicrystals. Based on a generalized multiple-length-scale Landau theory, SPSM first evaluates various spectral configurations of candidate structures under a hard constraint. It then identifies the configuration with the lowest free energy. Using this optimal configuration, SPSM calculates phase diagrams to explore the thermodynamic stability of desired quasicrystals. SPSM can design a minimal Landau theory capable of stabilizing the desired quasicrystals by incrementally increasing the number of length scales. Our application of SPSM has not only confirmed known behaviors in 10-and 12-fold quasicrystals but also led to a significant prediction that quasicrystals with 8-, 14-, 16-, and 18-fold symmetry could be stable within three-length-scale Landau models.
Quasicrystals are intriguing ordered structures characterized by quasiperiodic translational and noncrystallographic rotational symmetry. The tiling of different geometric units such as triangles and squares in two-dimensional space can result in a great variety of quasicrystals that could be realized by the self-assembly of liquid crystalline molecules. In this study, we introduce three self-similar dodecagonal tilings, including a novel diamond–square–triangle pattern, composed of triangular and quadrangular tiles, and examine their thermodynamic stability by using the self-consistent field theory applied to T-shaped liquid crystalline molecules. Specifically, we detail the inflation rules for the construction of these dodecagonal tilings, analyze their self-similarity, and show that these tilings can be viewed as projections of higher-dimensional periodic lattice points with projection windows. Using these dodecagonal tilings as initial configurations of the SCFT results in solutions corresponding to quasicrystals that could form from T-shaped liquid crystalline molecules. The relative stability of these aperiodic phases is analyzed to obtain design rules that could stabilize quasicrystals. Meanwhile, we provide a criterion for distinguishing three dodecagonal quasicrystals and their approximants by analyzing their diffraction peaks. These findings shed new light on the discovery of new quasicrystals in soft materials.
In this paper, we propose a new algorithm, the irrational-window-filter projection method (IWFPM), for quasiperiodic systems with concentrated spectral point distribution. Based on the projection method (PM), IWFPM filters out dominant spectral points by defining an irrational window and uses a corresponding index-shift transform to make the FFT available. The error analysis on the function approximation level is also given. We apply IWFPM to one-dimensional, two-dimensional (2D), and three-dimensional (3D) quasiperiodic Schro'‘textbackslashdinger eigenproblems (QSEs) to demonstrate its accuracy and efficiency. IWFPM exhibits a significant computational advantage over PM for both extended and localized quantum states. More importantly, by using IWFPM, the existence of Anderson localization in 2D and 3D QSEs is numerically verified.
数字生态指数是北京大学大数据分析与应用技术国家工程实验室联合校内外多方共同开展的研究项目,将为数字中国建设提供科学评估工具,也为促进地方数字经济发展、营造良好数字生态环境提供实践抓手。
在张平文院士的领衔指导下,基于中国科学院学部工作局院士课题、发改委重大研究系列课题、网信办委托课题等研究基础,实验室于2020年开始连续四年发布《数字生态指数报告》。
相关学术研究成果在《电子政务》特约专刊发表,在政届、学界和业界都产生了较高影响力。
围绕“生态视角引领规制建设激发数据活力”的主题分享了观点,认为数字生态包括数字基础、数字能力、数字应用和数字规则四个一级指标。在数字生态视角之下,能够更好地建立数字规制、激发要素活力,实现理论与实践的相互促进,从而加快推动数据要素市场的建设和发展。首先介绍数字经济发展的时代背景以及国家的相关政策,接下来阐述激活数据要素价值过程中所需经历的数据要素化、价值化、资产化等重要步骤,最后就其中的规划、人才、场景、合规、协作等问题给出建议,探索通过流通交易、协同赋能、多源融合等模式来进一步激活数据要素价值,促进经济高质量发展。
围绕“生态视角引领规制建设激发数据活力”的主题分享了观点,认为数字生态包括数字基础、数字能力、数字应用和数字规则四个一级指标。在数字生态视角之下,能够更好地建立数字规制、激发要素活力,实现理论与实践的相互促进,从而加快推动数据要素市场的建设和发展。
首先通过若干理论探讨和客观现象来阐述数字经济的重要性,然后对数字经济领域中的几个重要问题,即数据生产要素特征、数字化转型规律、以及数字经济如何评估等进行深入分析,并强调构建数字生态的重要性,最后对北京大学在数字经济和数字生态方面已经开展的一些工作做简要介绍。
首先对武汉大学学科建设的目标、特色、理念,观念等方面进行梳理,然后结合武汉大学2023年“学科建设年”具体行动,从人才培养、队伍建设、科学研究、体制机制改革等四个方面重点介绍武汉大学优化学科布局,探索学科交叉研究和交叉学科发展模式等一系列加强学科建设的举措和成效,最后强调,学科发展要以党建引领、资源配置协同、治理体系完善、大学精神凝心铸魂为实践保障。
从应用数学的价值观与发展历史说起,阐述什么是机理与数据的融合计算及其特点和意义,然后通过智慧气象预报与AI for Social Science两个方面来介绍如何有效地结合具体场景来应用机理与数据的融合计算,最后分析了融合计算对应用数学的影响,并探讨如何加强相关体制机制的建设来促进机理与数据融合计算的发展。
首先简要介绍数字化时代对人类、社会和国家的影响以及目前北大在数字化方面的理论探索进展,然后详细阐述北京大学在数智化建设方面所取得的成果,之后对教育数智化进行思考,探索教育与数智化的关系、数智化对教育的影响以及教育应该对数智化发展所起的引导作用,最后对教育数智化的未来发展提出了若干建议。
本报告首先从几个日常问题切入,揭示“计算在当前已经与生产生活密不可分”的结论,进而简要介绍数学和计算相互交融的历史进程和发展现状,接下来详细阐述计算的几个要素(数据、算法、算力和场景)所具有的特点、新的时代特征和数学在其中的重要作用等,最后对计算与数学共进的未来进行展望。
2020 - CSIAM Transactions on Applied Mathematics (Editor in Chief)
2014 - Multiscale Modeling & Simulation, A SIAM Interdisciplinary Journal
2013 - Science China Mathematics
2012 - Discrete and Continuous Dynamical System-B
2011 - Journal of Mathematics in Industry (Coordinating Editors)
2010 - Applied Mathematics and Mechanics;(Associate Chief Editor Since 2014)
2007 - Journal of Computational Mathematics
2006 - Communications in Computational Physics
2006 - International Journal of Nonlinear Science
2005 - Communication in Mathematical Sciences
2005 - Journal of Information and Computational Science
2005 - 2013 SIAM Journal on Numerical Analysis
2002 - Applied Mathematical Research Express (AMRX)
2010 - Advances in Mathematics
2007 - 《工程数学学报》
2006 - 《数学杂志》
2004 - 《计算数学》
2004 - 《计算物理》
2004 - 《东北数学》
李英女士