复杂流体环境中纳米颗粒的反常扩散及其操控

薛春东; 郑旭; 胡国庆

doi:10.6052/1000-0992-26-004

复杂流体环境中纳米颗粒的反常扩散及其操控

doi: 10.6052/1000-0992-26-004 cstr: 32046.14.1000-0992-26-004

1.
大连理工大学, 116024, 大连
2.
浙江大学, 310058, 杭州
3.
中国科学院力学研究所, 100190, 北京

基金项目: 国家基金委重点研发计划课题 (2024YFA1209900, 2022YFF0503500), 国家自然科学基金 (12532012, 12172081, 12472273) 项目资助. 感谢殷一帆、徐潇宇两位同学在文献整理和图表绘制方面给予的支持.

详细信息

作者简介:
薛春东, 大连理工大学副教授、博士生导师. 本科毕业于山东大学, 博士毕业于中国科学院力学研究所, 2017年入职大连理工大学. 研究方向为微纳流体力学基础及应用. 主持国家自然科学基金、国家重点研发计划子课题、中国博士后科学基金、辽宁省自然科学基金等项目. 在微纳流体力学及相关领域期刊发表论文50余篇, 授权专利10余件. 担任中国力学学会−微纳尺度流动专业组组员、《水动力学研究与进展》和Journal of Hydrodynamics期刊编委

通讯作者:
ghu@zju.edu.cn

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- 被引次数: 0
出版历程
- 收稿日期: 2026-01-24
- 录用日期: 2026-05-15
- 网络出版日期: 2026-06-02

Anomalous Diffusion and Manipulation of Nanoparticles in Complex Fluid Environments

1.
Dalian University of Technology, Dalian 116024, China
2.
Zhejiang University, Hangzhou 310058, China
3.
Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China

More Information

Corresponding author: ghu@zju.edu.cn

摘要

摘要: 复杂流体环境中纳米颗粒的扩散行为广泛存在于自然和工业过程中. 不同于经典布朗扩散, 复杂流体环境中纳米颗粒呈现反常扩散特性, 其机理认识及操控方法在生物、物理、医学及工程等多个领域具有重要科学意义和应用价值. 本文系统回顾了复杂流体环境中纳米颗粒反常扩散的研究进展. 首先, 阐释反常扩散超越经典布朗运动的核心特征, 梳理主要的理论框架与研究方法; 其次, 具体介绍亚扩散、超扩散、布朗非高斯扩散等三类具体反常扩散的机制及模型, 并从力学与统计物理耦合的角度, 探讨基于外场作用和智能设计的扩散行为调控机制; 最后, 总结该领域在建模、实验解析及应用中的关键挑战与发展方向.
- 复杂流体 /
- 反常扩散 /
- 纳米颗粒 /
- 输运操控
Abstract: The diffusive behavior of nanoparticles in complex fluid environments is widely observed in natural and industrial processes. In contrast to classical Brownian diffusion, nanoparticles in complex fluids exhibit anomalous diffusion characteristics. Understanding its mechanisms and developing control approaches hold significant scientific importance and application value across fields such as biology, physics, medicine, and engineering. This article provides a systematic review of the research progress on anomalous diffusion of nanoparticles in complex fluid environments. First, the core features of anomalous diffusion that go beyond classical Brownian motion are elucidated, and the main theoretical frameworks and research methods are outlined. Second, mechanisms and models of three specific anomalous diffusion, i.e., subdiffusion, superdiffusion, and Brownian yet non-Gaussian diffusion, are introduced in detail. The regulation mechanisms of diffusion behavior based on external field effects and intelligent design are also explored from the perspective of coupling mechanics and statistical physics. Finally, key challenges and future directions in modeling, experimental analysis, and applications in this field are summarized.
- complex fluids /
- anomalous diffusion /
- nanoparticles /
- transport manipulation

HTML全文

图 1 复杂流体环境中纳米颗粒反常扩散的物理图像、统计特征与研究框架示意图. 左侧示意纳米颗粒在细胞质、高分子网络、多孔介质等复杂流体环境中的运动情形, 这些介质通常具有结构异质性、黏弹性或动态不均匀性. 中间给出了反常扩散的典型统计特征, 包括均方位移 (MSD) 随时间的非线性标度关系 (亚扩散、正常扩散与超扩散) 以及位移概率分布 (DPD) 偏离高斯分布的情形. 右侧总结了反常扩散的主要力学机制、理论模型与操控途径, 包括时间记忆效应、空间约束与异质性、输运系数涨落以及非平衡驱动, 并对应分数布朗运动 (FBM)、连续时间随机游走 (CTRW)、扩散性−扩散系数 (DD) 和莱维飞行 (LF) 模型, 同时展示了外场调控等实现扩散行为可控调制的思路

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图 2 反常扩散典型研究方法示意图. (A)单粒子追踪 (SPT) 技术的装置设计及典型的三维粒子轨迹用于获取纳米颗粒在复杂环境中的单轨迹信息(Bucci et al. 2024); (B)基于单粒子动态光散射 (DLS) 技术的纳米粒子形状分析(Guerra et al. 2019); (C) 荧光相关光谱 (FCS) 技术原理、装置及数据分析(Yu et al. 2021); (D) 基于分子动力学模拟 (MD) 方法的聚合物网络结构及纳米颗粒扩散轨迹(Dai et al. 2022); (E) 第二届Andi挑战赛基本任务设置(Muñoz-Gil et al. 2025); (F) 基于机器学习方法的“扩散指纹”构建及反常扩散特征分析流程(Pinholt et al. 2021).

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图 3 复杂介质中亚扩散行为的典型实验观测、理论模型与物理机制示意. (A) 聚合物溶液中的记忆效应导致纳米颗粒扩散的 MSD 随时间呈幂律标度增长(Lim and Jeon 2025); (B) 细胞质的自组织效应抑制纳米颗粒的扩散, 导致扩散变慢以及扩散指数降低(Huang et al. 2022); (C) 受纳米粒子形状影响的细胞膜上三种扩散模式及相应轨迹(Choo et al. 2021); (D) 机器学习辅助的广义朗之万方程 (GLE) 模拟方法流程图(Russo et al. 2024); (E)细胞质中的大分子拥挤及多尺度障碍示意图(Destrian et al. 2025); (F) SPT结果展示海马神经元轴突起始段的纳米隔室及纳米颗粒受限扩散轨迹(Albrecht et al. 2016). 该图强调了时间非局域记忆效应与空间异质性是亚扩散产生的两类主要物理来源.

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图 4 复杂环境中布朗非高斯扩散 (BYND) 与超扩散行为的代表性实验与统计特征. (A) BYND 扩散中单粒子轨迹、MSD 近似线性增长以及位移分布呈非高斯长尾的典型结果(Wang et al. 2012); (B)从阿米巴虫 (Amoebas) 运动到秃鹰 (Vulture) 飞行等过程中线性MSD部分均存在非高斯成分(Vilk et al. 2022); (C) 不同流动条件下响应性弹性凝胶中自驱动纳米颗粒的运动轨迹及对应的多阶段MSD曲线 (Goswami et al. 2024); (D)在高度密集的活性细菌悬浮液中示踪粒子呈现超级扩散行为, 且超扩散的强度与细菌的活性密度直接相关(Xie et al. 2022).

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图 5 通过外加物理场实现纳米颗粒反常扩散行为调控的典型策略示意. (A) 磁场作用下磁性纳米颗粒在沿推进方向的扩散有所增强, 其扩散系数与电场频率相关, 且可以通过改变系统参数来精确控制(Stoop et al. 2019); (B) 外加电场可显著增强或抑制微通道中纳米颗粒的集体扩散行为(Wang et al. 2022); (C) 通过使用光学加热的金纳米结构在液体中产生强烈的局部温度梯度, 实现单个胶体粒子捕获(Braun and Cichos 2013); (D) 通过红外激光点加热在溶液中构建温度梯度, 实现基于热泳机制的纳米级外泌体快速高效富集 (Liu et al. 2019); (E) 不同过氧化氢浓度溶液下, 自驱动纳米颗粒的典型运动轨迹及对应MSD结果对比(Howse et al. 2007). (F) Janus式光驱动自推进管状纳米机器人在紫外光和蓝光照射下能实现多种运动模式(Ussia et al. 2022).

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参考文献(311)

[1]	Ahmadzadegan A, Mitra H, Vlachos P P, Ardekani A M. 2023. Particle image micro-rheology (PIR) using displacement probability density function. J. Rheol., 67: 823. doi: 10.1122/8.0000629 Ahmadzadegan A, Mitra H, Vlachos P P, Ardekani A M. 2023. Particle image micro-rheology (PIR) using displacement probability density function. J. Rheol., 67: 823. doi: 10.1122/8.0000629
[2]	Akimoto T, Jeon J H, Metzler R, Miyaguchi T, Uneyama T, Yamamoto E. 2026. Anomalous statistics in the Langevin equation with ﬂuctuating diffusivity: from brownian yet non-Gaussian diffusion to anomalous diffusion and ergodicity breaking. Rep. Prog. Phys., 89: 014602. doi: 10.1088/1361-6633/AE358C Akimoto T, Jeon J H, Metzler R, Miyaguchi T, Uneyama T, Yamamoto E. 2026. Anomalous statistics in the Langevin equation with ﬂuctuating diffusivity: from brownian yet non-Gaussian diffusion to anomalous diffusion and ergodicity breaking. Rep. Prog. Phys., 89: 014602. doi: 10.1088/1361-6633/AE358C
[3]	Albrecht D, Winterflood C M, Sadeghi M, Tschager T, Noé F, Ewers H. 2016. Nanoscopic compartmentalization of membrane protein motion at the axon initial segment. J. Cell Biol., 215: 37-46. doi: 10.1083/jcb.201603108 Albrecht D, Winterflood C M, Sadeghi M, Tschager T, Noé F, Ewers H. 2016. Nanoscopic compartmentalization of membrane protein motion at the axon initial segment. J. Cell Biol., 215: 37-46. doi: 10.1083/jcb.201603108
[4]	Arcizet D, Meier B, Sackmann E, Rädler J O, Heinrich D. 2008. Temporal analysis of active and passive transport in living cells. Phys. Rev. Lett., 101: 248103. Arcizet D, Meier B, Sackmann E, Rädler J O, Heinrich D. 2008. Temporal analysis of active and passive transport in living cells. Phys. Rev. Lett., 101: 248103.
[5]	Arts M, Smal I, Paul M W, Wyman C, Meijering E. 2019. Particle mobility analysis using deep learning and the moment scaling spectrum. Sci. Rep., 9: 17160. doi: 10.1038/s41598-019-53663-8 Arts M, Smal I, Paul M W, Wyman C, Meijering E. 2019. Particle mobility analysis using deep learning and the moment scaling spectrum. Sci. Rep., 9: 17160. doi: 10.1038/s41598-019-53663-8
[6]	Ashkin A. 1997. Optical trapping and manipulation of neutral particles using lasers. Proc. Natl. Acad. Sci. U. S. A., 94: 4853-4860. Ashkin A. 1997. Optical trapping and manipulation of neutral particles using lasers. Proc. Natl. Acad. Sci. U. S. A., 94: 4853-4860.
[7]	Ault J T, Shin S. 2025. Physicochemical hydrodynamics of particle diffusiophoresis driven by chemical gradients. Annu. Rev. Fluid Mech., 57: 227-255. Ault J T, Shin S. 2025. Physicochemical hydrodynamics of particle diffusiophoresis driven by chemical gradients. Annu. Rev. Fluid Mech., 57: 227-255.
[8]	Bancaud A, Huet S, Daigle N, Mozziconacci J, Beaudouin J, Ellenberg J. 2009. Molecular crowding affects diffusion and binding of nuclear proteins in heterochromatin and reveals the fractal organization of chromatin. EMBO J., 28: 3785-3798. doi: 10.1038/emboj.2009.340 Bancaud A, Huet S, Daigle N, Mozziconacci J, Beaudouin J, Ellenberg J. 2009. Molecular crowding affects diffusion and binding of nuclear proteins in heterochromatin and reveals the fractal organization of chromatin. EMBO J., 28: 3785-3798. doi: 10.1038/emboj.2009.340
[9]	Banks D S, Fradin C. 2005. Anomalous diffusion of proteins due to molecular crowding. Biophys. J., 89: 2960-2971. doi: 10.1529/biophysj.104.051078 Banks D S, Fradin C. 2005. Anomalous diffusion of proteins due to molecular crowding. Biophys. J., 89: 2960-2971. doi: 10.1529/biophysj.104.051078
[10]	Banks D S, Tressler C, Peters R D, Hofling F, Fradin C. 2016. Characterizing anomalous diffusion in crowded polymer solutions and gels over five decades in time with variable-lengthscale fluorescence correlation spectroscopy. Soft Matter, 12: 4190-4203. doi: 10.1039/c5sm01213a Banks D S, Tressler C, Peters R D, Hofling F, Fradin C. 2016. Characterizing anomalous diffusion in crowded polymer solutions and gels over five decades in time with variable-lengthscale fluorescence correlation spectroscopy. Soft Matter, 12: 4190-4203. doi: 10.1039/c5sm01213a
[11]	Barkai E, Burov S. 2020. Packets of diffusing particles exhibit universal exponential tails. Phys. Rev. Lett., 124: 060603. doi: 10.1103/PhysRevLett.124.060603 Barkai E, Burov S. 2020. Packets of diffusing particles exhibit universal exponential tails. Phys. Rev. Lett., 124: 060603. doi: 10.1103/PhysRevLett.124.060603
[12]	Barr J J, Auro R, Sam-Soon N, Kassegne S, Peters G, Bonilla N, Hatay M, Mourtada S, Bailey B, Youle M, Felts B, Baljon A, Nulton J, Salamon P, Rohwer F. 2015. Subdiffusive motion of bacteriophage in mucosal surfaces increases the frequency of bacterial encounters. Proc. Natl. Acad. Sci. U. S. A., 112: 13675-13680. Barr J J, Auro R, Sam-Soon N, Kassegne S, Peters G, Bonilla N, Hatay M, Mourtada S, Bailey B, Youle M, Felts B, Baljon A, Nulton J, Salamon P, Rohwer F. 2015. Subdiffusive motion of bacteriophage in mucosal surfaces increases the frequency of bacterial encounters. Proc. Natl. Acad. Sci. U. S. A., 112: 13675-13680.
[13]	Bauer T, Höfling F, Munk T, Frey E, Franosch T. 2010. The localization transition of the two-dimensional lorentz model. Eur. Phys. J. Spec. Top., 189: 103-118. Bauer T, Höfling F, Munk T, Frey E, Franosch T. 2010. The localization transition of the two-dimensional lorentz model. Eur. Phys. J. Spec. Top., 189: 103-118.
[14]	Bechinger C, Di Leonardo R, Löwen H, Reichhardt C, Volpe Giorgio, Volpe Giovanni. 2016. Active particles in complex and crowded environments. Rev. Mod. Phys., 88: 045006. Bechinger C, Di Leonardo R, Löwen H, Reichhardt C, Volpe Giorgio, Volpe Giovanni. 2016. Active particles in complex and crowded environments. Rev. Mod. Phys., 88: 045006.
[15]	Bénichou O, Bodrova A, Chakraborty D, Illien P, Law A, Mejía-Monasterio C, Oshanin G, Voituriez R. 2013. Geometry-induced superdiffusion in driven crowded systems. Phys. Rev. Lett., 111: 260601. Bénichou O, Bodrova A, Chakraborty D, Illien P, Law A, Mejía-Monasterio C, Oshanin G, Voituriez R. 2013. Geometry-induced superdiffusion in driven crowded systems. Phys. Rev. Lett., 111: 260601.
[16]	Bénichou O, Chevalier C, Klafter J, Meyer B, Voituriez R. 2010. Geometry-controlled kinetics. Nat. Chem., 2: 472-477. Bénichou O, Chevalier C, Klafter J, Meyer B, Voituriez R. 2010. Geometry-controlled kinetics. Nat. Chem., 2: 472-477.
[17]	Benichou O, Chevalier C, Meyer B, Voituriez R. 2011. Facilitated diffusion of proteins on chromatin. Phys. Rev. Lett., 106: 038102. Benichou O, Chevalier C, Meyer B, Voituriez R. 2011. Facilitated diffusion of proteins on chromatin. Phys. Rev. Lett., 106: 038102.
[18]	Berg H C, Brown D A. 1972. Chemotaxis in escherichia coli analysed by three-dimensional tracking. Nature, 239: 500-504. Berg H C, Brown D A. 1972. Chemotaxis in escherichia coli analysed by three-dimensional tracking. Nature, 239: 500-504.
[19]	Berkowitz B, Scher H. 1998. Theory of anomalous chemical transport in random fracture networks. Phys. Rev. E, 57: 5858-5869. Berkowitz B, Scher H. 1998. Theory of anomalous chemical transport in random fracture networks. Phys. Rev. E, 57: 5858-5869.
[20]	Blanco E, Shen H, Ferrari M. 2015. Principles of nanoparticle design for overcoming biological barriers to drug delivery. Nat. Biotech., 33: 941-951. Blanco E, Shen H, Ferrari M. 2015. Principles of nanoparticle design for overcoming biological barriers to drug delivery. Nat. Biotech., 33: 941-951.
[21]	Bouchaud J P, Georges A. 1990. Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications. Phys. Rep., 195: 127-293. Bouchaud J P, Georges A. 1990. Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications. Phys. Rep., 195: 127-293.
[22]	Brackley C A, Cates M E, Marenduzzo D. 2013. Intracellular facilitated diffusion: searchers, crowders, and blockers. Phys. Rev. Lett., 111: 108101. Brackley C A, Cates M E, Marenduzzo D. 2013. Intracellular facilitated diffusion: searchers, crowders, and blockers. Phys. Rev. Lett., 111: 108101.
[23]	Brangwynne C P, Mitchison T J, Hyman A A. 2011. Active liquid-like behavior of nucleoli determines their size and shape in xenopus laevis oocytes. Proc. Natl. Acad. Sci. U. S. A., 108: 4334-4339. Brangwynne C P, Mitchison T J, Hyman A A. 2011. Active liquid-like behavior of nucleoli determines their size and shape in xenopus laevis oocytes. Proc. Natl. Acad. Sci. U. S. A., 108: 4334-4339.
[24]	Braun M, Cichos F. 2013. Optically controlled thermophoretic trapping of single nano-objects. ACS Nano, 7: 11200-11208. doi: 10.1021/nn404980k Braun M, Cichos F. 2013. Optically controlled thermophoretic trapping of single nano-objects. ACS Nano, 7: 11200-11208. doi: 10.1021/nn404980k
[25]	Brochard Wyart F, de Gennes P G. 2000. Viscosity at small scales in polymer melts. Eur. Phys. J. E, 1: 93-97. doi: 10.1007/s101890050011 Brochard Wyart F, de Gennes P G. 2000. Viscosity at small scales in polymer melts. Eur. Phys. J. E, 1: 93-97. doi: 10.1007/s101890050011
[26]	Bucci A, Tortarolo G, Held M O, Bega L, Perego E, Castagnetti F, Bozzoni I, Slenders E, Vicidomini G. 2024. 4D Single-particle tracking with asynchronous read-out single-photon avalanche diode array detector. Nat. Commun., 15: 6188. doi: 10.1038/s41467-024-50512-9 Bucci A, Tortarolo G, Held M O, Bega L, Perego E, Castagnetti F, Bozzoni I, Slenders E, Vicidomini G. 2024. 4D Single-particle tracking with asynchronous read-out single-photon avalanche diode array detector. Nat. Commun., 15: 6188. doi: 10.1038/s41467-024-50512-9
[27]	Burov S, Jeon J H, Metzler R, Barkai E. 2011. Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking. Phys. chem. chem. phys., 13: 1800-1812. doi: 10.1039/c0cp01879a Burov S, Jeon J H, Metzler R, Barkai E. 2011. Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking. Phys. chem. chem. phys., 13: 1800-1812. doi: 10.1039/c0cp01879a
[28]	Cahn D, Stern A, Buckenmeyer M, Wolf M, Duncan G A. 2024. Extracellular matrix limits nanoparticle diffusion and cellular uptake in a tissue-specific manner. ACS Nano, 18: 32045-32055. doi: 10.1021/acsnano.4c10381 Cahn D, Stern A, Buckenmeyer M, Wolf M, Duncan G A. 2024. Extracellular matrix limits nanoparticle diffusion and cellular uptake in a tissue-specific manner. ACS Nano, 18: 32045-32055. doi: 10.1021/acsnano.4c10381
[29]	Cai L H, Panyukov S, Rubinstein M. 2011. Mobility of spherical probe objects in polymer liquids. Macromolecules, 44: 7853-7863. Cai L H, Panyukov S, Rubinstein M. 2011. Mobility of spherical probe objects in polymer liquids. Macromolecules, 44: 7853-7863.
[30]	Cai L H, Panyukov S, Rubinstein M. 2015. Hopping diffusion of nanoparticles in polymer matrices. Macromolecules, 48: 847-862. doi: 10.1021/ma501608x Cai L H, Panyukov S, Rubinstein M. 2015. Hopping diffusion of nanoparticles in polymer matrices. Macromolecules, 48: 847-862. doi: 10.1021/ma501608x
[31]	Cai W J, Hu Y, Qu X, Zhao H, Wang G Y, Li J, Huang Z H. 2025. Machine learning analysis of anomalous diffusion. Eur. Phys. J. Plus, 140: 183. Cai W J, Hu Y, Qu X, Zhao H, Wang G Y, Li J, Huang Z H. 2025. Machine learning analysis of anomalous diffusion. Eur. Phys. J. Plus, 140: 183.
[32]	Casalegno M, Raos G, Appetecchi G B, Passerini S, Castiglione F, Mele A. 2017. From nanoscale to microscale: crossover in the diffusion dynamics within two pyrrolidinium-based ionic liquids. J. Phys. Chem. Lett., 8: 5196-5202. doi: 10.1021/acs.jpclett.7b02431 Casalegno M, Raos G, Appetecchi G B, Passerini S, Castiglione F, Mele A. 2017. From nanoscale to microscale: crossover in the diffusion dynamics within two pyrrolidinium-based ionic liquids. J. Phys. Chem. Lett., 8: 5196-5202. doi: 10.1021/acs.jpclett.7b02431
[33]	Caspi A, Granek R, Elbaum M. 2000. Enhanced diffusion in active intracellular transport. Phys. Rev. Lett., 85: 5655-5658. Caspi A, Granek R, Elbaum M. 2000. Enhanced diffusion in active intracellular transport. Phys. Rev. Lett., 85: 5655-5658.
[34]	Cates M E, Tailleur J. 2015. Motility-induced phase separation. Annu. Rev. Condens. Matter Phys., 6: 219-244. doi: 10.1103/MBRL-V75B Cates M E, Tailleur J. 2015. Motility-induced phase separation. Annu. Rev. Condens. Matter Phys., 6: 219-244. doi: 10.1103/MBRL-V75B
[35]	Chakrabarti R, Kesselheim S, Kosovan P, Holm C. 2013. Tracer diffusion in a crowded cylindrical channel. Phys. Rev. E, 87: 062709. Chakrabarti R, Kesselheim S, Kosovan P, Holm C. 2013. Tracer diffusion in a crowded cylindrical channel. Phys. Rev. E, 87: 062709.
[36]	Chakraborty I, Roichman Y. 2020. Disorder-induced fickian, yet non-gaussian diffusion in heterogeneous media. Phys. Rev. Res., 2: 022020. Chakraborty I, Roichman Y. 2020. Disorder-induced fickian, yet non-gaussian diffusion in heterogeneous media. Phys. Rev. Res., 2: 022020.
[37]	Charbonneau P, Jin Y L, Parisi G, Zamponi F. 2014. Hopping and the stokes-einstein relation breakdown in simple glass formers. Proc. Natl. Acad. Sci. U. S. A., 111: 15025-15030. doi: 10.1073/pnas.1417182111 Charbonneau P, Jin Y L, Parisi G, Zamponi F. 2014. Hopping and the stokes-einstein relation breakdown in simple glass formers. Proc. Natl. Acad. Sci. U. S. A., 111: 15025-15030. doi: 10.1073/pnas.1417182111
[38]	Chaudhuri P, Berthier L, Kob W. 2007. Universal nature of particle displacements close to glass and jamming transitions. Phys. Rev. Lett., 99: 060604. Chaudhuri P, Berthier L, Kob W. 2007. Universal nature of particle displacements close to glass and jamming transitions. Phys. Rev. Lett., 99: 060604.
[39]	Chauhan V P, Stylianopoulos T, Boucher Y, Jain R K. 2011. Delivery of molecular and nanoscale medicine to tumors: transport barriers and strategies. Annu. Rev. Chem. Biomol. Eng., 2: 281-298. Chauhan V P, Stylianopoulos T, Boucher Y, Jain R K. 2011. Delivery of molecular and nanoscale medicine to tumors: transport barriers and strategies. Annu. Rev. Chem. Biomol. Eng., 2: 281-298.
[40]	Chechkin A V, Seno F, Metzler R, Sokolov I M. 2017. Brownian yet non-gaussian diffusion: from superstatistics to subordination of diffusing diffusivities. Phys. Rev. X, 7: 021002. doi: 10.1103/PhysRevX.7.021002 Chechkin A V, Seno F, Metzler R, Sokolov I M. 2017. Brownian yet non-gaussian diffusion: from superstatistics to subordination of diffusing diffusivities. Phys. Rev. X, 7: 021002. doi: 10.1103/PhysRevX.7.021002
[41]	Chen D T, Weeks E R, Crocker J C, Islam M F, Verma R, Gruber J, Levine A J, Lubensky T C, Yodh A G. 2003. Rheological microscopy: local mechanical properties from microrheology. Phys. Rev. Lett., 90: 108301. Chen D T, Weeks E R, Crocker J C, Islam M F, Verma R, Gruber J, Levine A J, Lubensky T C, Yodh A G. 2003. Rheological microscopy: local mechanical properties from microrheology. Phys. Rev. Lett., 90: 108301.
[42]	Chen P Y, Huang Z H, Liang J S, Cui T Q, Zhang X H, Miao B, Yan L T. 2016. Diffusion and directionality of charged nanoparticles on lipid bilayer membrane. ACS Nano, 10: 11541-11547. Chen P Y, Huang Z H, Liang J S, Cui T Q, Zhang X H, Miao B, Yan L T. 2016. Diffusion and directionality of charged nanoparticles on lipid bilayer membrane. ACS Nano, 10: 11541-11547.
[43]	Chen W, Liang Y J, Hu S, Sun H G. 2015. Fractional derivative anomalous diffusion equation modeling prime number distribution. Fract. Calc. Appl. Anal., 18: 789-798. doi: 10.1515/fca-2015-0047 Chen W, Liang Y J, Hu S, Sun H G. 2015. Fractional derivative anomalous diffusion equation modeling prime number distribution. Fract. Calc. Appl. Anal., 18: 789-798. doi: 10.1515/fca-2015-0047
[44]	Chen W, Sun, H G, Zhang X D, Korosak D. 2010. Anomalous diffusion modeling by fractal and fractional derivatives. Comput. Math. App., 59: 1754-1758. Chen W, Sun, H G, Zhang X D, Korosak D. 2010. Anomalous diffusion modeling by fractal and fractional derivatives. Comput. Math. App., 59: 1754-1758.
[45]	Chen Y L, Xiang Z J, Ren H Z, Guo F Q, Ganesan V, Liu J. 2024. Anisotropic and non-gaussian diffusion of thin nanorods in polymer networks. Macromolecules, 57: 5105-5118. doi: 10.1021/acs.macromol.4c00635 Chen Y L, Xiang Z J, Ren H Z, Guo F Q, Ganesan V, Liu J. 2024. Anisotropic and non-gaussian diffusion of thin nanorods in polymer networks. Macromolecules, 57: 5105-5118. doi: 10.1021/acs.macromol.4c00635
[46]	Cherstvy A G, Chechkin A V, Metzler R. 2013. Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes. New J. Phys., 15: 083039. Cherstvy A G, Chechkin A V, Metzler R. 2013. Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes. New J. Phys., 15: 083039.
[47]	Cherstvy A G, Metzler R. 2013. Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes. Phys. Chem. Chem. Phys., 15: 20220-20235. doi: 10.1039/c3cp53056f Cherstvy A G, Metzler R. 2013. Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes. Phys. Chem. Chem. Phys., 15: 20220-20235. doi: 10.1039/c3cp53056f
[48]	Cherstvy A G, Thapa S, Wagner C E, Metzler R. 2019. Non-gaussian, non-ergodic, and non-fickian diffusion of tracers in mucin hydrogels. Soft Matter, 15: 2526-2551. doi: 10.1039/c8sm02096e Cherstvy A G, Thapa S, Wagner C E, Metzler R. 2019. Non-gaussian, non-ergodic, and non-fickian diffusion of tracers in mucin hydrogels. Soft Matter, 15: 2526-2551. doi: 10.1039/c8sm02096e
[49]	Choo P, Liu T T, Odom T W. 2021. Nanoparticle shape determines dynamics of targetingnanoconstructs on cell membranes. J. Am. Chem. Soc., 143: 4550-4555. Choo P, Liu T T, Odom T W. 2021. Nanoparticle shape determines dynamics of targetingnanoconstructs on cell membranes. J. Am. Chem. Soc., 143: 4550-4555.
[50]	Chubynsky M V, Slater G W. 2014. Diffusing diffusivity: a model for anomalous, yet brownian, diffusion. Phys. Rev. Lett., 113: 098302. Chubynsky M V, Slater G W. 2014. Diffusing diffusivity: a model for anomalous, yet brownian, diffusion. Phys. Rev. Lett., 113: 098302.
[51]	Ciocanel M V, Ding L, Mastromatteo L, Reichheld S, Cabral S, Mowry, K, Sandstede B. 2024. Parameter identifiability in PDE models of fluorescence recovery after photobleaching. Bull. Math. Biol., 86: 36. Ciocanel M V, Ding L, Mastromatteo L, Reichheld S, Cabral S, Mowry, K, Sandstede B. 2024. Parameter identifiability in PDE models of fluorescence recovery after photobleaching. Bull. Math. Biol., 86: 36.
[52]	Crocker J C, Valentine M T, Weeks E R, Gisler T, Kaplan P D, Yodh A G, Weitz D A. 2000. Two-point microrheology of inhomogeneous soft materials. Phys. Rev. Lett., 85: 888-891. Crocker J C, Valentine M T, Weeks E R, Gisler T, Kaplan P D, Yodh A G, Weitz D A. 2000. Two-point microrheology of inhomogeneous soft materials. Phys. Rev. Lett., 85: 888-891.
[53]	Dai X B, Zhang X Y, Gao L J, Xu Z Y, Yan L T. 2022. Topology mediates transport of nanoparticles in macromolecular networks. Nat. Commun., 13: 4094. doi: 10.1038/s41467-022-31861-9 Dai X B, Zhang X Y, Gao L J, Xu Z Y, Yan L T. 2022. Topology mediates transport of nanoparticles in macromolecular networks. Nat. Commun., 13: 4094. doi: 10.1038/s41467-022-31861-9
[54]	Dai Y K, Zhang R L, Sun W X, Wang T, Chen Y H, Tong Z. 2021. Dynamical heterogeneity in the gelation process of a polymer solution with a lower critical solution temperature. Soft Matter, 17: 3222-3233. Dai Y K, Zhang R L, Sun W X, Wang T, Chen Y H, Tong Z. 2021. Dynamical heterogeneity in the gelation process of a polymer solution with a lower critical solution temperature. Soft Matter, 17: 3222-3233.
[55]	Das A, Sengupta P, Khanam J, Augustine R, Thakor A S, Thomas S, Roy S, Ghosal K. 2025. Magnetic nanoparticle as a new cutting-edge drug delivery and diagnostic platform: a review on its properties, synthesis, surface modification and applications. Carbohydr. Polym. Tech., 11: 100905. Das A, Sengupta P, Khanam J, Augustine R, Thakor A S, Thomas S, Roy S, Ghosal K. 2025. Magnetic nanoparticle as a new cutting-edge drug delivery and diagnostic platform: a review on its properties, synthesis, surface modification and applications. Carbohydr. Polym. Tech., 11: 100905.
[56]	Daumas F, Destainville N, Millot C, Lopez A, Dean D, Salomé L. 2003. Confined diffusion without fences of a G-protein-coupled receptor as revealed by single particle tracking. Biophys. J., 84: 356-366. Daumas F, Destainville N, Millot C, Lopez A, Dean D, Salomé L. 2003. Confined diffusion without fences of a G-protein-coupled receptor as revealed by single particle tracking. Biophys. J., 84: 356-366.
[57]	Dell Z E, Schweizer K S. 2014. Theory of localization and activated hopping of nanoparticles in cross-linked networks and entangled polymer melts. Macromolecules, 47: 405-414. Dell Z E, Schweizer K S. 2014. Theory of localization and activated hopping of nanoparticles in cross-linked networks and entangled polymer melts. Macromolecules, 47: 405-414.
[58]	Démery V, Bénichou O, Jacquin H. 2014. Generalized langevin equations for a driven tracer in dense soft colloids: construction and applications. New J. Phys., 16: 053032. doi: 10.1088/1367-2630/16/5/053032 Démery V, Bénichou O, Jacquin H. 2014. Generalized langevin equations for a driven tracer in dense soft colloids: construction and applications. New J. Phys., 16: 053032. doi: 10.1088/1367-2630/16/5/053032
[59]	Destrian O, Moisan N, Mege R M, Ladoux B, Goyeau B, Chabanon M. 2026. Cytoplasmic crowding acts as a porous medium reducing macromolecule diffusion. Proc. Natl. Acad. Sci. U. S. A., 123: e2519599123. doi: 10.1073/PNAS.2519599123 Destrian O, Moisan N, Mege R M, Ladoux B, Goyeau B, Chabanon M. 2026. Cytoplasmic crowding acts as a porous medium reducing macromolecule diffusion. Proc. Natl. Acad. Sci. U. S. A., 123: e2519599123. doi: 10.1073/PNAS.2519599123
[60]	Dey K K, Sen A. 2017. Chemically propelled molecules and machines. J. Am. Chem. Soc., 139: 7666-7676. Dey K K, Sen A. 2017. Chemically propelled molecules and machines. J. Am. Chem. Soc., 139: 7666-7676.
[61]	Dix J A, Verkman A S. 2008. Crowding effects on diffusion in solutions and cells. Annu. Rev. Biophys., 37: 247-263. doi: 10.1146/annurev.biophys.37.032807.12582410.1146/annurev.biophys.37.032807.125824 Dix J A, Verkman A S. 2008. Crowding effects on diffusion in solutions and cells. Annu. Rev. Biophys., 37: 247-263. doi: 10.1146/annurev.biophys.37.032807.12582410.1146/annurev.biophys.37.032807.125824
[62]	Drechsler M, Giavazzi F, Cerbino R, Palacios I M. 2017. Active diffusion and advection in drosophila oocytes result from the interplay of actin and microtubules. Nat. Commun., 8: 1520. Drechsler M, Giavazzi F, Cerbino R, Palacios I M. 2017. Active diffusion and advection in drosophila oocytes result from the interplay of actin and microtubules. Nat. Commun., 8: 1520.
[63]	Du Y F, Jiang H J, Hou Z H. 2019. Study of active brownian particle diffusion in polymer solutions. Soft Matter, 15: 2020-2031. doi: 10.1039/c8sm02292e Du Y F, Jiang H J, Hou Z H. 2019. Study of active brownian particle diffusion in polymer solutions. Soft Matter, 15: 2020-2031. doi: 10.1039/c8sm02292e
[64]	Dunkel J, Heidenreich S, Drescher K, Wensink H H, Bär M, Goldstein R E. 2013. Fluid dynamics of bacterial turbulence. Phys. Rev. Lett., 110: 228102. Dunkel J, Heidenreich S, Drescher K, Wensink H H, Bär M, Goldstein R E. 2013. Fluid dynamics of bacterial turbulence. Phys. Rev. Lett., 110: 228102.
[65]	Einstein A. 1905. On the movement of small particles suspended in stationary liquids required by the molecular-kinetic theory of heat. Ann. Phys., 15: 549-560. Einstein A. 1905. On the movement of small particles suspended in stationary liquids required by the molecular-kinetic theory of heat. Ann. Phys., 15: 549-560.
[66]	Ernst D, Hellmann M, Köhler J, Weiss M. 2012. Fractional brownian motion in crowded fluids. Soft Matter, 8: 4886. Ernst D, Hellmann M, Köhler J, Weiss M. 2012. Fractional brownian motion in crowded fluids. Soft Matter, 8: 4886.
[67]	Ernst D, Kohler J, Weiss M. 2014. Probing the type of anomalous diffusion with single-particle tracking. Phys. Chem. Chem. Phys., 16: 7686-7691. Ernst D, Kohler J, Weiss M. 2014. Probing the type of anomalous diffusion with single-particle tracking. Phys. Chem. Chem. Phys., 16: 7686-7691.
[68]	Eshghi I, Zidovska A, Grosberg A Y. 2023. Activity-driven phase transition causes coherent flows of chromatin. Phys. Rev. Lett., 131: 048401. Eshghi I, Zidovska A, Grosberg A Y. 2023. Activity-driven phase transition causes coherent flows of chromatin. Phys. Rev. Lett., 131: 048401.
[69]	Evers F, Hanes R D L, Zunke C, Capellmann R F, Bewerunge J, Dalle-Ferrier C, Jenkins M C, Ladadwa I, Heuer A, Castañeda-Priego R, Egelhaaf S U. 2013. Colloids in light fields: particle dynamics in random and periodic energy landscapes. Eur. Phys. J. Spec. Top., 222: 2995-3009. Evers F, Hanes R D L, Zunke C, Capellmann R F, Bewerunge J, Dalle-Ferrier C, Jenkins M C, Ladadwa I, Heuer A, Castañeda-Priego R, Egelhaaf S U. 2013. Colloids in light fields: particle dynamics in random and periodic energy landscapes. Eur. Phys. J. Spec. Top., 222: 2995-3009.
[70]	Falkovich G, Gawedzki K, Vergassola M. 2001. Particles and fields in fluid turbulence. Rev. Mod. Phys., 73: 913-975. Falkovich G, Gawedzki K, Vergassola M. 2001. Particles and fields in fluid turbulence. Rev. Mod. Phys., 73: 913-975.
[71]	Felfoul O, Mohammadi M, Taherkhani S, de Lanauze D, Xu Y Z, Loghin D, Essa S, Jancik S, Houle D, Lafleur M, Gaboury L, Tabrizian M, Kaou N, Atkin M, Vuong T, Batist G, Beauchemin N, Radzioch D, Martel S. 2016. Magneto-aerotactic bacteria deliver drug-containing nanoliposomes to tumour hypoxic regions. Nat. Nanotechnol., 11: 941-947. Felfoul O, Mohammadi M, Taherkhani S, de Lanauze D, Xu Y Z, Loghin D, Essa S, Jancik S, Houle D, Lafleur M, Gaboury L, Tabrizian M, Kaou N, Atkin M, Vuong T, Batist G, Beauchemin N, Radzioch D, Martel S. 2016. Magneto-aerotactic bacteria deliver drug-containing nanoliposomes to tumour hypoxic regions. Nat. Nanotechnol., 11: 941-947.
[72]	Feng C Q, Si X H, Li B T, Cao L M, Zhu J. 2021. An inverse problem to simulate the transport of chloride in concrete by time–space fractional diffusion model. Inverse Probl. Sci. Eng., 29: 2429-2445. Feng C Q, Si X H, Li B T, Cao L M, Zhu J. 2021. An inverse problem to simulate the transport of chloride in concrete by time–space fractional diffusion model. Inverse Probl. Sci. Eng., 29: 2429-2445.
[73]	Fernández Fernández G, Manzo C, Lewenstein M, Dauphin A, Muñoz Gil G. 2024. Learning minimal representations of stochastic processes with variational autoencoders. Phys. Rev. E, 110: L012102. doi: 10.1103/PhysRevE.110.L012102 Fernández Fernández G, Manzo C, Lewenstein M, Dauphin A, Muñoz Gil G. 2024. Learning minimal representations of stochastic processes with variational autoencoders. Phys. Rev. E, 110: L012102. doi: 10.1103/PhysRevE.110.L012102
[74]	Fodor É, Guo M, Gov N S, Visco P, Weitz D A, van Wijland F. 2015. Activity-driven fluctuations in living cells. Europhys. Lett., 110: 48005. doi: 10.1209/0295-5075/110/48005 Fodor É, Guo M, Gov N S, Visco P, Weitz D A, van Wijland F. 2015. Activity-driven fluctuations in living cells. Europhys. Lett., 110: 48005. doi: 10.1209/0295-5075/110/48005
[75]	Forte G, Cecconi F, Vulpiani A. 2014. Non-anomalous diffusion is not always Gaussian. Eur. Phys. J. B., 87: 102. Forte G, Cecconi F, Vulpiani A. 2014. Non-anomalous diffusion is not always Gaussian. Eur. Phys. J. B., 87: 102.
[76]	Fujiwara T K, Iwasawa K, Kalay Z, Tsunoyama T A, Watanabe Y, Umemura Y M, Murakoshi H, Suzuki K G N, Nemoto Y L, Morone N, Kusumi A. 2016. Confined diffusion of transmembrane proteins and lipids induced by the same actin meshwork lining the plasma membrane. Mol. Biol. Cell., 27: 1101-1119. Fujiwara T K, Iwasawa K, Kalay Z, Tsunoyama T A, Watanabe Y, Umemura Y M, Murakoshi H, Suzuki K G N, Nemoto Y L, Morone N, Kusumi A. 2016. Confined diffusion of transmembrane proteins and lipids induced by the same actin meshwork lining the plasma membrane. Mol. Biol. Cell., 27: 1101-1119.
[77]	Gao Y, Kilfoil M L. 2007. Direct imaging of dynamical heterogeneities near the colloid-gel transition. Phys. Rev. Lett., 99: 078301. Gao Y, Kilfoil M L. 2007. Direct imaging of dynamical heterogeneities near the colloid-gel transition. Phys. Rev. Lett., 99: 078301.
[78]	Ge T, Grest G S, Rubinstein M. 2018. Nanorheology of entangled polymer melts. Phys. Rev. Lett., 120: 057801. doi: 10.1103/PhysRevLett.120.057801 Ge T, Grest G S, Rubinstein M. 2018. Nanorheology of entangled polymer melts. Phys. Rev. Lett., 120: 057801. doi: 10.1103/PhysRevLett.120.057801
[79]	Ghomian T, Hihath J. 2023. Review of dielectrophoretic manipulation of micro and nanomaterials: fundamentals, recent developments, and challenges. IEEE Trans. Biomed. Eng., 70: 27-41. doi: 10.1109/TBME.2022.3183167 Ghomian T, Hihath J. 2023. Review of dielectrophoretic manipulation of micro and nanomaterials: fundamentals, recent developments, and challenges. IEEE Trans. Biomed. Eng., 70: 27-41. doi: 10.1109/TBME.2022.3183167
[80]	Ghosh S K, Cherstvy A G, Metzler R. 2015. Non-universal tracer diffusion in crowded media of non-inert obstacles. Phys. Chem. Chem. Phys., 17: 1847-1858. Ghosh S K, Cherstvy A G, Metzler R. 2015. Non-universal tracer diffusion in crowded media of non-inert obstacles. Phys. Chem. Chem. Phys., 17: 1847-1858.
[81]	Gnesotto F, Mura F, Gladrow J, Broedersz C P. 2018. Broken detailed balance and non-equilibrium dynamics in living systems. Rep. Prog. Phys., 81: 066601. Gnesotto F, Mura F, Gladrow J, Broedersz C P. 2018. Broken detailed balance and non-equilibrium dynamics in living systems. Rep. Prog. Phys., 81: 066601.
[82]	Golding I, Cox E C. 2006. Physical nature of bacterial cytoplasm. Phys. Rev. Lett., 96: 098102. Golding I, Cox E C. 2006. Physical nature of bacterial cytoplasm. Phys. Rev. Lett., 96: 098102.
[83]	Goldstein R E, Van De Meent J W. 2015. A physical perspective on cytoplasmic streaming. Interface Focus, 5: 20150030. Goldstein R E, Van De Meent J W. 2015. A physical perspective on cytoplasmic streaming. Interface Focus, 5: 20150030.
[84]	Goldstein R E. 2015. Green algae as model organisms for biological fluid dynamics. Annu. Rev. Fluid Mech., 47: 343-375. doi: 10.1146/annurev-fluid-010313-141426 Goldstein R E. 2015. Green algae as model organisms for biological fluid dynamics. Annu. Rev. Fluid Mech., 47: 343-375. doi: 10.1146/annurev-fluid-010313-141426
[85]	Goswami K, Cherstvy A G, Godec A, Metzler R. 2024. Anomalous diffusion of active brownian particles in responsive elastic gels: nonergodicity, non-gaussianity, and distributions of trapping times. Phys. Rev. E, 110: 044609. doi: 10.1103/PhysRevE.110.044609 Goswami K, Cherstvy A G, Godec A, Metzler R. 2024. Anomalous diffusion of active brownian particles in responsive elastic gels: nonergodicity, non-gaussianity, and distributions of trapping times. Phys. Rev. E, 110: 044609. doi: 10.1103/PhysRevE.110.044609
[86]	Goychuk I. 2009. Viscoelastic subdiffusion: From anomalous to normal. Phys. Rev. E, 80: 046125. Goychuk I. 2009. Viscoelastic subdiffusion: From anomalous to normal. Phys. Rev. E, 80: 046125.
[87]	Grier D G. 2003. A revolution in optical manipulation. Nature, 424: 810-816. doi: 10.1038/nature01935 Grier D G. 2003. A revolution in optical manipulation. Nature, 424: 810-816. doi: 10.1038/nature01935
[88]	Guan J, Wang B, Granick S. 2014. Even hard-sphere colloidal suspensions display fickian yet non-gaussian diffusion. ACS Nano, 8: 3331-3336. Guan J, Wang B, Granick S. 2014. Even hard-sphere colloidal suspensions display fickian yet non-gaussian diffusion. ACS Nano, 8: 3331-3336.
[89]	Guerra L F, Muir T W, Yang H. 2019. Single-particle dynamic light scattering: shapes of individual nanoparticles. Nano Lett., 19: 5530-5536. Guerra L F, Muir T W, Yang H. 2019. Single-particle dynamic light scattering: shapes of individual nanoparticles. Nano Lett., 19: 5530-5536.
[90]	Guigas G, Kalla C, Weiss M. 2007. Probing the nanoscale viscoelasticity of intracellular fluids in living cells. Biophys. J., 93: 316-323. Guigas G, Kalla C, Weiss M. 2007. Probing the nanoscale viscoelasticity of intracellular fluids in living cells. Biophys. J., 93: 316-323.
[91]	Guo M, Ehrlicher A J, Jensen M H, Renz M, Moore J R, Goldman R D, Lippincott-Schwartz J, Mackintosh F C, Weitz D A. 2014. Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy. Cell, 158: 822-832. Guo M, Ehrlicher A J, Jensen M H, Renz M, Moore J R, Goldman R D, Lippincott-Schwartz J, Mackintosh F C, Weitz D A. 2014. Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy. Cell, 158: 822-832.
[92]	Han D, Korabel N, Chen R, Johnston M, Gavrilova A, Allan V J, Fedotov S, Waigh T A. 2020. Deciphering anomalous heterogeneous intracellular transport with neural networks. eLife, 9: e52224. doi: 10.7554/eLife.52224 Han D, Korabel N, Chen R, Johnston M, Gavrilova A, Allan V J, Fedotov S, Waigh T A. 2020. Deciphering anomalous heterogeneous intracellular transport with neural networks. eLife, 9: e52224. doi: 10.7554/eLife.52224
[93]	Hao P T, Li S S, Xue C D, Qin K R. 2025. Spatial heterogeneity in hydrogels: nanoparticle diffusivity as a probe for network dynamics. Microchem. J., 214: 114092. doi: 10.1016/j.microc.2025.114092 Hao P T, Li S S, Xue C D, Qin K R. 2025. Spatial heterogeneity in hydrogels: nanoparticle diffusivity as a probe for network dynamics. Microchem. J., 214: 114092. doi: 10.1016/j.microc.2025.114092
[94]	Harris T H, Banigan E J, Christian D A, Konradt C, Tait Wojno E D, Norose K, Wilson E H, John B, Weninger W, Luster A D, Liu A J, Hunter C A. 2012. Generalized lévy walks and the role of chemokines in migration of effector CD8 + T cells. Nature, 486: 545-548. doi: 10.1038/nature11098 Harris T H, Banigan E J, Christian D A, Konradt C, Tait Wojno E D, Norose K, Wilson E H, John B, Weninger W, Luster A D, Liu A J, Hunter C A. 2012. Generalized lévy walks and the role of chemokines in migration of effector CD8 + T cells. Nature, 486: 545-548. doi: 10.1038/nature11098
[95]	Havlin S, Ben-Avraham D. 1987. Diffusion in disordered media. Adv. Phys., 36: 695-798. doi: 10.1063/5.0272370 Havlin S, Ben-Avraham D. 1987. Diffusion in disordered media. Adv. Phys., 36: 695-798. doi: 10.1063/5.0272370
[96]	He K, Babaye Khorasani F, Retterer S T, Thomas D K, Conrad J C, Krishnamoorti R. 2013. Diffusive dynamics of nanoparticles in arrays of nanoposts. ACS Nano, 7: 5122-5130. He K, Babaye Khorasani F, Retterer S T, Thomas D K, Conrad J C, Krishnamoorti R. 2013. Diffusive dynamics of nanoparticles in arrays of nanoposts. ACS Nano, 7: 5122-5130.
[97]	He W, Song H, Su Y, Geng L, Ackerson B J, Peng H B, Tong P. 2016. Dynamic heterogeneity and non-gaussian statistics for acetylcholine receptors on live cell membrane. Nat. Commun., 7: 11701. He W, Song H, Su Y, Geng L, Ackerson B J, Peng H B, Tong P. 2016. Dynamic heterogeneity and non-gaussian statistics for acetylcholine receptors on live cell membrane. Nat. Commun., 7: 11701.
[98]	He X C, Yang Y Y, Han Y L, Cao C Y, Zhang Z B, Li L X, Xiao C L, Guo H, Wang L, Han L C, Qu Z G, Liu N, Han S, Xu F. 2023. Extracellular matrix physical properties govern the diffusion of nanoparticles in tumor microenvironment. Proc. Natl. Acad. Sci. U. S. A., 120: e2209260120. He X C, Yang Y Y, Han Y L, Cao C Y, Zhang Z B, Li L X, Xiao C L, Guo H, Wang L, Han L C, Qu Z G, Liu N, Han S, Xu F. 2023. Extracellular matrix physical properties govern the diffusion of nanoparticles in tumor microenvironment. Proc. Natl. Acad. Sci. U. S. A., 120: e2209260120.
[99]	He Y, Burov S, Metzler R, Barkai E. 2008. Random time-scale invariant diffusion and transport coefficients. Phys. Rev. Lett., 101: 058101. He Y, Burov S, Metzler R, Barkai E. 2008. Random time-scale invariant diffusion and transport coefficients. Phys. Rev. Lett., 101: 058101.
[100]	Heckert A, Dahal L, Tjian R, Darzacq X. 2022. Recovering mixtures of fast-diffusing states from short single-particle trajectories. eLife, 11: e70169. Heckert A, Dahal L, Tjian R, Darzacq X. 2022. Recovering mixtures of fast-diffusing states from short single-particle trajectories. eLife, 11: e70169.
[101]	Hedges L O, Jack R L, Garrahan J P, Chandler D. 2009. Dynamic order-disorder in atomistic models of structural glass formers. Science, 323: 1309-1313. doi: 10.1126/science.1166665 Hedges L O, Jack R L, Garrahan J P, Chandler D. 2009. Dynamic order-disorder in atomistic models of structural glass formers. Science, 323: 1309-1313. doi: 10.1126/science.1166665
[102]	Heinemann F, Vogel S K, Schwille P. 2013. Lateral membrane diffusion modulated by a minimal actin cortex. Biophys. J., 104: 1465-1475. doi: 10.1016/j.bpj.2013.02.042 Heinemann F, Vogel S K, Schwille P. 2013. Lateral membrane diffusion modulated by a minimal actin cortex. Biophys. J., 104: 1465-1475. doi: 10.1016/j.bpj.2013.02.042
[103]	Höfling F, Franosch T, Frey E. 2006. Localization transition of the three-dimensional lorentz model and continuum percolation. Phys. Rev. Lett., 96: 165901. Höfling F, Franosch T, Frey E. 2006. Localization transition of the three-dimensional lorentz model and continuum percolation. Phys. Rev. Lett., 96: 165901.
[104]	Höfling F, Franosch T. 2013. Anomalous transport in the crowded world of biological cells. Rep. Prog. Phys., 76: 046602. doi: 10.1088/0034-4885/76/4/046602 Höfling F, Franosch T. 2013. Anomalous transport in the crowded world of biological cells. Rep. Prog. Phys., 76: 046602. doi: 10.1088/0034-4885/76/4/046602
[105]	Hoshino T, Murakami D, Tanaka Y, Takata M, Jinnai H, Takahara A. 2013. Dynamical crossover between hyperdiffusion and subdiffusion of polymer-grafted nanoparticles in a polymer matrix. Phys. Rev. E, 88: 032602. Hoshino T, Murakami D, Tanaka Y, Takata M, Jinnai H, Takahara A. 2013. Dynamical crossover between hyperdiffusion and subdiffusion of polymer-grafted nanoparticles in a polymer matrix. Phys. Rev. E, 88: 032602.
[106]	Hou S, Exell J, Welsher K. 2020. Real-time 3D single molecule tracking. Nat. Commun., 11: 3607. Hou S, Exell J, Welsher K. 2020. Real-time 3D single molecule tracking. Nat. Commun., 11: 3607.
[107]	Howse J R, Jones R A L, Ryan A J, Gough T, Vafabakhsh R, Golestanian R. 2007. Self-motile colloidal particles: from directed propulsion to random walk. Phys. Rev. Lett., 99: 048102. Howse J R, Jones R A L, Ryan A J, Gough T, Vafabakhsh R, Golestanian R. 2007. Self-motile colloidal particles: from directed propulsion to random walk. Phys. Rev. Lett., 99: 048102.
[108]	Huang W Y C, Cheng X, Ferrell J E. 2022. Cytoplasmic organization promotes protein diffusion in xenopus extracts. Nat. Commun., 13: 5599. doi: 10.1038/s41467-022-33339-0 Huang W Y C, Cheng X, Ferrell J E. 2022. Cytoplasmic organization promotes protein diffusion in xenopus extracts. Nat. Commun., 13: 5599. doi: 10.1038/s41467-022-33339-0
[109]	Hurtado P I, Berthier L, Kob W. 2007. Heterogeneous diffusion in a reversible gel. Phys. Rev. Lett., 98: 135503. Hurtado P I, Berthier L, Kob W. 2007. Heterogeneous diffusion in a reversible gel. Phys. Rev. Lett., 98: 135503.
[110]	Jain R, Sebastian K L. 2017. Diffusing diffusivity: Rotational diffusion in two and three dimensions. J. Chem. Phys., 146: 214102. Jain R, Sebastian K L. 2017. Diffusing diffusivity: Rotational diffusion in two and three dimensions. J. Chem. Phys., 146: 214102.
[111]	Jamali V, Hargus C, Ben Moshe A, Aghazadeh A, Ha H D, Mandadapu K K, Alivisatos A P. 2021. Anomalous nanoparticle surface diffusion in LCTEM is revealed by deep learning-assisted analysis. Proc. Natl. Acad. Sci. U. S. A., 118: e2017616118. Jamali V, Hargus C, Ben Moshe A, Aghazadeh A, Ha H D, Mandadapu K K, Alivisatos A P. 2021. Anomalous nanoparticle surface diffusion in LCTEM is revealed by deep learning-assisted analysis. Proc. Natl. Acad. Sci. U. S. A., 118: e2017616118.
[112]	Javer A, Long Z C, Nugent E, Grisi M, Siriwatwetchakul K, Dorfman K D, Cicuta P, Cosentino Lagomarsino M. 2013. Short-time movement of E. coli chromosomal loci depends on coordinate and subcellular localization. Nat. Commun., 4: 3003. Javer A, Long Z C, Nugent E, Grisi M, Siriwatwetchakul K, Dorfman K D, Cicuta P, Cosentino Lagomarsino M. 2013. Short-time movement of E. coli chromosomal loci depends on coordinate and subcellular localization. Nat. Commun., 4: 3003.
[113]	Jeon J H, Javanainen M, Martinez-Seara H, Metzler R, Vattulainen I. 2016. Protein crowding in lipid bilayers gives rise to non-gaussian anomalous lateral diffusion of phospholipids and proteins. Phys. Rev. X, 6: 021006. Jeon J H, Javanainen M, Martinez-Seara H, Metzler R, Vattulainen I. 2016. Protein crowding in lipid bilayers gives rise to non-gaussian anomalous lateral diffusion of phospholipids and proteins. Phys. Rev. X, 6: 021006.
[114]	Jeon J H, Leijnse N, Oddershede L B, Metzler R. 2013. Anomalous diffusion and power-law relaxation of the time averaged mean squared displacement in worm-like micellar solutions. New J. Phys., 15: 045011. Jeon J H, Leijnse N, Oddershede L B, Metzler R. 2013. Anomalous diffusion and power-law relaxation of the time averaged mean squared displacement in worm-like micellar solutions. New J. Phys., 15: 045011.
[115]	Jeon J H, Tejedor V, Burov S, Barkai E, Selhuber Unkel C, Berg Sorensen K, Oddershede L, Metzler R. 2011. In vivo anomalous diffusion and weak ergodicity breaking of lipid granules. Phys. Rev. Lett., 106: 048103. Jeon J H, Tejedor V, Burov S, Barkai E, Selhuber Unkel C, Berg Sorensen K, Oddershede L, Metzler R. 2011. In vivo anomalous diffusion and weak ergodicity breaking of lipid granules. Phys. Rev. Lett., 106: 048103.
[116]	Jiang C, Luo H Y, Xu X P, Dou S X, Li W, Guan D S, Ye F F, Chen X S, Guo M, Wang P Y, Li H. 2023. Switch of cell migration modes orchestrated by changes of three-dimensional lamellipodium structure and intracellular diffusion. Nat. Commun., 14: 5166. doi: 10.1038/s41467-023-40858-x Jiang C, Luo H Y, Xu X P, Dou S X, Li W, Guan D S, Ye F F, Chen X S, Guo M, Wang P Y, Li H. 2023. Switch of cell migration modes orchestrated by changes of three-dimensional lamellipodium structure and intracellular diffusion. Nat. Commun., 14: 5166. doi: 10.1038/s41467-023-40858-x
[117]	Jiang L, Granick S. 2017. Real-space, in situ maps of hydrogel pores. ACS Nano, 11: 204-212. Jiang L, Granick S. 2017. Real-space, in situ maps of hydrogel pores. ACS Nano, 11: 204-212.
[118]	Joseph K, Igor M S. 2005. Anomalous diffusion spreads its wings. Phys. World., 18: 29. Joseph K, Igor M S. 2005. Anomalous diffusion spreads its wings. Phys. World., 18: 29.
[119]	Joseph Phillies G D. 2015. In complex fluids the gaussian diffusion approximation is generally invalid. Soft Matter, 11: 580-586. doi: 10.1039/c4sm02506g Joseph Phillies G D. 2015. In complex fluids the gaussian diffusion approximation is generally invalid. Soft Matter, 11: 580-586. doi: 10.1039/c4sm02506g
[120]	Joshi K, York H M, Wright C S, Biswas R R, Arumugam S, Iyer-Biswas S. 2024. Emergent spatiotemporal organization in stochastic intracellular transport dynamics. Annu. Rev. Biophys., 53: 193-220. doi: 10.1146/ANNUREV-BIOPHYS-030422-044448 Joshi K, York H M, Wright C S, Biswas R R, Arumugam S, Iyer-Biswas S. 2024. Emergent spatiotemporal organization in stochastic intracellular transport dynamics. Annu. Rev. Biophys., 53: 193-220. doi: 10.1146/ANNUREV-BIOPHYS-030422-044448
[121]	Juan M L, Righini M, Quidant R. 2011. Plasmon nano-optical tweezers. Nat. Photon., 5: 349-356. Juan M L, Righini M, Quidant R. 2011. Plasmon nano-optical tweezers. Nat. Photon., 5: 349-356.
[122]	Kalathi J T, Yamamoto U, Schweizer K S, Grest G S, Kumar S K. 2014. Nanoparticle diffusion in polymer nanocomposites. Phys. Rev. Lett., 112: 108301. Kalathi J T, Yamamoto U, Schweizer K S, Grest G S, Kumar S K. 2014. Nanoparticle diffusion in polymer nanocomposites. Phys. Rev. Lett., 112: 108301.
[123]	Kantor Y, Kardar M. 2004. Anomalous dynamics of forced translocation. Phys. Rev. E, 69: 021806. Kantor Y, Kardar M. 2004. Anomalous dynamics of forced translocation. Phys. Rev. E, 69: 021806.
[124]	Kegel W K. 2000. Direct observation of dynamical heterogeneities in colloidal hard-sphere suspensions. Science, 287: 290-293. doi: 10.1126/science.287.5451.290 Kegel W K. 2000. Direct observation of dynamical heterogeneities in colloidal hard-sphere suspensions. Science, 287: 290-293. doi: 10.1126/science.287.5451.290
[125]	Khair A S, Squires T M. 2009. The influence of hydrodynamic slip on the electrophoretic mobility of a spherical colloidal particle. Phys. Fluids, 21: 042001. Khair A S, Squires T M. 2009. The influence of hydrodynamic slip on the electrophoretic mobility of a spherical colloidal particle. Phys. Fluids, 21: 042001.
[126]	Kim J, Kim C, Sung B J. 2013. Simulation study of seemingly fickian but heterogeneous dynamics of two dimensional colloids. Phys. Rev. Lett., 110: 047801. Kim J, Kim C, Sung B J. 2013. Simulation study of seemingly fickian but heterogeneous dynamics of two dimensional colloids. Phys. Rev. Lett., 110: 047801.
[127]	Kim K, Guo J H, Liang Z X, Fan D L. 2018. Artificial micro/nanomachines for bioapplications: biochemical delivery and diagnostic sensing. Adv. Funct. Mater., 28: 1705867. Kim K, Guo J H, Liang Z X, Fan D L. 2018. Artificial micro/nanomachines for bioapplications: biochemical delivery and diagnostic sensing. Adv. Funct. Mater., 28: 1705867.
[128]	Korabel N, Waigh T A. 2025. Deep learning for heterogeneous anomalous dynamics in cellular and molecular biology. Cell Rep. Phys. Sci., 6: 102891. Korabel N, Waigh T A. 2025. Deep learning for heterogeneous anomalous dynamics in cellular and molecular biology. Cell Rep. Phys. Sci., 6: 102891.
[129]	Kostko A F, Anisimov M A, Sengers J V. 2007. Dynamics of critical fluctuations in polymer solutions. Phys. Rev. E, 76: 021804. Kostko A F, Anisimov M A, Sengers J V. 2007. Dynamics of critical fluctuations in polymer solutions. Phys. Rev. E, 76: 021804.
[130]	Kou S C, Xie X S. 2004. Generalized langevin equation with fractional gaussian noise: subdiffusion within a single protein molecule. Phys. Rev. Lett., 93: 180603. Kou S C, Xie X S. 2004. Generalized langevin equation with fractional gaussian noise: subdiffusion within a single protein molecule. Phys. Rev. Lett., 93: 180603.
[131]	Kowalek P, Loch Olszewska H, Szwabiński J. 2019. Classification of diffusion modes in single-particle tracking data: feature-based versus deep-learning approach. Phys. Rev. E, 100: 032410. Kowalek P, Loch Olszewska H, Szwabiński J. 2019. Classification of diffusion modes in single-particle tracking data: feature-based versus deep-learning approach. Phys. Rev. E, 100: 032410.
[132]	Kozlov A S, Andor-Ardo D, Hudspeth A J. 2012. Anomalous brownian motion discloses viscoelasticity in the ear’s mechanoelectrical-transduction apparatus. Proc. Natl. Acad. Sci. U. S. A., 109: 2896-2901. doi: 10.1073/pnas.1121389109 Kozlov A S, Andor-Ardo D, Hudspeth A J. 2012. Anomalous brownian motion discloses viscoelasticity in the ear’s mechanoelectrical-transduction apparatus. Proc. Natl. Acad. Sci. U. S. A., 109: 2896-2901. doi: 10.1073/pnas.1121389109
[133]	Kumar Y, Sinha A S K, Nigam K D P, Dwivedi D, Sangwai J S. 2023. Functionalized nanoparticles: tailoring properties through surface energetics and coordination chemistry for advanced biomedical applications. Nanoscale, 15: 6075-6104. doi: 10.1039/d2nr07163k Kumar Y, Sinha A S K, Nigam K D P, Dwivedi D, Sangwai J S. 2023. Functionalized nanoparticles: tailoring properties through surface energetics and coordination chemistry for advanced biomedical applications. Nanoscale, 15: 6075-6104. doi: 10.1039/d2nr07163k
[134]	Kusumi A, Fujiwara T K, Chadda R, Xie M, Tsunoyama T A, Kalay Z, Kasai R S, Suzuki K G N. 2012. Dynamic organizing principles of the plasma membrane that regulate signal transduction: commemorating the fortieth anniversary of singer and nicolson's fluid-mosaic model. Annu. Rev. Cell Dev. Biol., 28: 215-250. doi: 10.1146/annurev-cellbio-100809-151736 Kusumi A, Fujiwara T K, Chadda R, Xie M, Tsunoyama T A, Kalay Z, Kasai R S, Suzuki K G N. 2012. Dynamic organizing principles of the plasma membrane that regulate signal transduction: commemorating the fortieth anniversary of singer and nicolson's fluid-mosaic model. Annu. Rev. Cell Dev. Biol., 28: 215-250. doi: 10.1146/annurev-cellbio-100809-151736
[135]	Kusumi A, Nakada C, Ritchie K, Murase K, Suzuki K, Murakoshi H, Kasai R S, Kondo J, Fujiwara T. 2005. Paradigm shift of the plasma membrane concept from the two-dimensional continuum fluid to the partitioned fluid: high-speed single-molecule tracking of membrane molecules. Annu. Rev. Biophys. Biomol. Struct., 34: 351-78. Kusumi A, Nakada C, Ritchie K, Murase K, Suzuki K, Murakoshi H, Kasai R S, Kondo J, Fujiwara T. 2005. Paradigm shift of the plasma membrane concept from the two-dimensional continuum fluid to the partitioned fluid: high-speed single-molecule tracking of membrane molecules. Annu. Rev. Biophys. Biomol. Struct., 34: 351-78.
[136]	Kusumi A, Sako Y, Yamamoto M. 1993. Confined lateral diffusion of membrane receptors as studied by single particle tracking (nanovid microscopy). Effects of calcium-induced differentiation in cultured epithelial cells. Biophys. J., 65: 2021-2040. doi: 10.1016/S0006-3495(93)81253-0 Kusumi A, Sako Y, Yamamoto M. 1993. Confined lateral diffusion of membrane receptors as studied by single particle tracking (nanovid microscopy). Effects of calcium-induced differentiation in cultured epithelial cells. Biophys. J., 65: 2021-2040. doi: 10.1016/S0006-3495(93)81253-0
[137]	Kwon G, Sung B J, Yethiraj A. 2014. Dynamics in crowded environments: is non-Gaussian Brownian diffusion normal? J. Phys. Chem. B, 118: 8128-8134. doi: 10.1021/jp5011617 Kwon G, Sung B J, Yethiraj A. 2014. Dynamics in crowded environments: is non-Gaussian Brownian diffusion normal? J. Phys. Chem. B, 118: 8128-8134. doi: 10.1021/jp5011617
[138]	Lai S K, Wang Y Y, Wirtz D, Hanes J. 2009. Micro- and macrorheology of mucus. Adv. Drug. Deliv. Rev., 61: 86-100. doi: 10.1016/j.addr.2008.09.012 Lai S K, Wang Y Y, Wirtz D, Hanes J. 2009. Micro- and macrorheology of mucus. Adv. Drug. Deliv. Rev., 61: 86-100. doi: 10.1016/j.addr.2008.09.012
[139]	Langevin P. 1908. Sur la théorie du mouvement brownien. C. R. Acad. Sci., 146: 530-533. Langevin P. 1908. Sur la théorie du mouvement brownien. C. R. Acad. Sci., 146: 530-533.
[140]	Langford G M. 1995. Actin- and microtubule-dependent organelle motors: interrelationships between the two motility systems. Curr. Opin. Cell Biol., 7: 82-88. Langford G M. 1995. Actin- and microtubule-dependent organelle motors: interrelationships between the two motility systems. Curr. Opin. Cell Biol., 7: 82-88.
[141]	Li D Z, Yao Q J, Huang Z H, 2021. WaveNet-based deep neural networks for the characterization of anomalous diffusion (WADNet). J. Phys. A: Math. Theor. , 54: 404003. Li D Z, Yao Q J, Huang Z H, 2021. WaveNet-based deep neural networks for the characterization of anomalous diffusion (WADNet). J. Phys. A: Math. Theor. , 54: 404003.
[142]	Li H, Dou S X, Liu Y R, Li W, Xie P, Wang, W C, Wang P Y. 2015. Mapping intracellular diffusion distribution using single quantum dot tracking: compartmentalized diffusion defined by endoplasmic reticulum. J. Am. Chem. Soc., 137: 436-44. Li H, Dou S X, Liu Y R, Li W, Xie P, Wang, W C, Wang P Y. 2015. Mapping intracellular diffusion distribution using single quantum dot tracking: compartmentalized diffusion defined by endoplasmic reticulum. J. Am. Chem. Soc., 137: 436-44.
[143]	Li W, Xu K. 2025. Super-resolution mapping and quantification of molecular diffusion via single-molecule displacement/diffusivity mapping (SMdM). Acc. Chem. Research, 58: 1224-1235. Li W, Xu K. 2025. Super-resolution mapping and quantification of molecular diffusion via single-molecule displacement/diffusivity mapping (SMdM). Acc. Chem. Research, 58: 1224-1235.
[144]	Lim C, Jeon J H. 2025. Anomalous diffusion in coupled viscoelastic media: a fractional langevin equation approach. Phys. Rev. Research, 7: 043356 Lim C, Jeon J H. 2025. Anomalous diffusion in coupled viscoelastic media: a fractional langevin equation approach. Phys. Rev. Research, 7: 043356
[145]	Liu C, Zhao J X, Tian F, Cai L L, Zhang W, Feng Q, Chang J Q, Wan F N, Yang Y J, Dai B, Cong Y L, Ding B Q, Sun J S, Tan W H. 2019. Low-cost thermophoretic profiling of extracellular-vesicle surface proteins for the early detection and classification of cancers. Nat. Biomed. Eng., 3: 183-193. doi: 10.1038/s41551-018-0343-6 Liu C, Zhao J X, Tian F, Cai L L, Zhang W, Feng Q, Chang J Q, Wan F N, Yang Y J, Dai B, Cong Y L, Ding B Q, Sun J S, Tan W H. 2019. Low-cost thermophoretic profiling of extracellular-vesicle surface proteins for the early detection and classification of cancers. Nat. Biomed. Eng., 3: 183-193. doi: 10.1038/s41551-018-0343-6
[146]	Lorentz H A. 1905. The motion of electrons in metallic bodies I. Proc. R. Netherlands Acad. Arts Sci., 7: 438-453. Lorentz H A. 1905. The motion of electrons in metallic bodies I. Proc. R. Netherlands Acad. Arts Sci., 7: 438-453.
[147]	Loverdo C, Bénichou O, Moreau M, Voituriez R. 2008. Enhanced reaction kinetics in biological cells. Nat. Phys., 4: 134-137. Loverdo C, Bénichou O, Moreau M, Voituriez R. 2008. Enhanced reaction kinetics in biological cells. Nat. Phys., 4: 134-137.
[148]	Lu J R, Robert D, Nguyen T H, Gallet F, Wilhelm C. 2010. In vivo determination of fluctuating forces during endosome trafficking using a combination of active and passive microrheology. PLoS One, 5: e10046. Lu J R, Robert D, Nguyen T H, Gallet F, Wilhelm C. 2010. In vivo determination of fluctuating forces during endosome trafficking using a combination of active and passive microrheology. PLoS One, 5: e10046.
[149]	Lu Q, Solomon M J. 2002. Probe size effects on the microrheology of associating polymer solutions. Phys. Rev. E, 66: 061504. Lu Q, Solomon M J. 2002. Probe size effects on the microrheology of associating polymer solutions. Phys. Rev. E, 66: 061504.
[150]	Luby-Phelps K, Mujumdar S, Mujumdar R B, Ernst L A, Galbraith W, Waggoner A S. 1993. A novel fluorescence ratiometric method confirms the low solvent viscosity of the cytoplasm. Biophys. J., 65: 236-242. Luby-Phelps K, Mujumdar S, Mujumdar R B, Ernst L A, Galbraith W, Waggoner A S. 1993. A novel fluorescence ratiometric method confirms the low solvent viscosity of the cytoplasm. Biophys. J., 65: 236-242.
[151]	Luby-Phelps K, Taylor D L, Lanni F. 1986. Probing the structure of cytoplasm. J. Cell Biol., 102: 2015-2022. Luby-Phelps K, Taylor D L, Lanni F. 1986. Probing the structure of cytoplasm. J. Cell Biol., 102: 2015-2022.
[152]	Lucas J S, Zhang Y J, Dudko O K, Murre C. 2014. 3D Trajectories adopted by coding and regulatory DNA elements: first-passage times for genomic interactions. Cell, 158: 339-352. Lucas J S, Zhang Y J, Dudko O K, Murre C. 2014. 3D Trajectories adopted by coding and regulatory DNA elements: first-passage times for genomic interactions. Cell, 158: 339-352.
[153]	Lutz E. 2001. Fractional langevin equation. Phys. Rev. E, 64: 051106. Lutz E. 2001. Fractional langevin equation. Phys. Rev. E, 64: 051106.
[154]	Magdziarz M, Weron A, Burnecki K, Klafter J. 2009. Fractional brownian motion versus the continuous-time random walk: a simple test for subdiffusive dynamics. Phys. Rev. Lett., 103: 180602. Magdziarz M, Weron A, Burnecki K, Klafter J. 2009. Fractional brownian motion versus the continuous-time random walk: a simple test for subdiffusive dynamics. Phys. Rev. Lett., 103: 180602.
[155]	Mandelbrot B B, Van Ness J W. 1968. Fractional brownian motions, fractional noises and applications. SIAM Rev., 10: 422-437. Mandelbrot B B, Van Ness J W. 1968. Fractional brownian motions, fractional noises and applications. SIAM Rev., 10: 422-437.
[156]	Mangalam M, Metzler R, Kelty-Stephen D G. 2023. Ergodic characterization of nonergodic anomalous diffusion processes. Phys. Rev. Research, 5: 023144. Mangalam M, Metzler R, Kelty-Stephen D G. 2023. Ergodic characterization of nonergodic anomalous diffusion processes. Phys. Rev. Research, 5: 023144.
[157]	Mankin R, Laas K, Lumi N. 2013. Memory effects for a trapped brownian particle in viscoelastic shear flows. Phys. Rev. E, 88: 042142. doi: 10.1103/PhysRevE.88.042142 Mankin R, Laas K, Lumi N. 2013. Memory effects for a trapped brownian particle in viscoelastic shear flows. Phys. Rev. E, 88: 042142. doi: 10.1103/PhysRevE.88.042142
[158]	Manzo C, Garcia-Parajo M F, 2015. A review of progress in single particle tracking: from methods to biophysical insights. Rep. Prog. Phys. , 78: 124601. Manzo C, Garcia-Parajo M F, 2015. A review of progress in single particle tracking: from methods to biophysical insights. Rep. Prog. Phys. , 78: 124601.
[159]	Manzo C, Torreno-Pina J A, Massignan P, Lapeyre G J, Lewenstein M, Garcia Parajo M F. 2015. Weak ergodicity breaking of receptor motion in living cells stemming from random diffusivity. Phys. Rev. X, 5: 011021. Manzo C, Torreno-Pina J A, Massignan P, Lapeyre G J, Lewenstein M, Garcia Parajo M F. 2015. Weak ergodicity breaking of receptor motion in living cells stemming from random diffusivity. Phys. Rev. X, 5: 011021.
[160]	Mao R F, Pretti E, Mittal J. 2021. Temperature-controlled reconfigurable nanoparticle binary superlattices. ACS Nano, 15: 8466-8473. Mao R F, Pretti E, Mittal J. 2021. Temperature-controlled reconfigurable nanoparticle binary superlattices. ACS Nano, 15: 8466-8473.
[161]	Marchetti M C, Joanny J F, Ramaswamy S, Liverpool T B, Prost J, Rao M, Simha R A. 2013. Hydrodynamics of soft active matter. Rev. Mod. Phys., 85: 1143-1189. Marchetti M C, Joanny J F, Ramaswamy S, Liverpool T B, Prost J, Rao M, Simha R A. 2013. Hydrodynamics of soft active matter. Rev. Mod. Phys., 85: 1143-1189.
[162]	Marel A K, Zorn M, Klingner C, Wedlich-Söldner R, Frey E, Rädler J O. 2014. Flow and diffusion in channel-guided cell migration. Biophys. J., 107: 1054-1064. Marel A K, Zorn M, Klingner C, Wedlich-Söldner R, Frey E, Rädler J O. 2014. Flow and diffusion in channel-guided cell migration. Biophys. J., 107: 1054-1064.
[163]	Marshall J S, 2016. A model of ultrasound-enhanced diffusion in a biofilm. J. Acoust. Soc. Am. , 139: EL228–EL233. Marshall J S, 2016. A model of ultrasound-enhanced diffusion in a biofilm. J. Acoust. Soc. Am. , 139: EL228–EL233.
[164]	Mason T G, Ganesan K, van Zanten J H, Wirtz D, Kuo S C. 1997. Particle tracking microrheology of complex fluids. Phys. Rev. Lett., 79: 3282-3285. doi: 10.1039/c6sm00769d Mason T G, Ganesan K, van Zanten J H, Wirtz D, Kuo S C. 1997. Particle tracking microrheology of complex fluids. Phys. Rev. Lett., 79: 3282-3285. doi: 10.1039/c6sm00769d
[165]	Mason T G, Weitz D A. 1995. Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids. Phys. Rev. Lett., 74: 1250-1253. Mason T G, Weitz D A. 1995. Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids. Phys. Rev. Lett., 74: 1250-1253.
[166]	Mejía Monasterio C, Metzler R, Vollmer J. 2020. Editorial: Anomalous transport: applications, mathematical perspectives, and big data. Front. Phys., 8: 622417. Mejía Monasterio C, Metzler R, Vollmer J. 2020. Editorial: Anomalous transport: applications, mathematical perspectives, and big data. Front. Phys., 8: 622417.
[167]	Meroz Y, Sokolov I M. 2015. A toolbox for determining subdiffusive mechanisms. Phys. Rep., 573: 1-29. doi: 10.1016/j.physrep.2015.01.002 Meroz Y, Sokolov I M. 2015. A toolbox for determining subdiffusive mechanisms. Phys. Rep., 573: 1-29. doi: 10.1016/j.physrep.2015.01.002
[168]	Metzler R, Jeon J H, Cherstvy A G, Barkai E. 2014. Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking. Phys. Chem. Chem. Phys., 16: 24128-24164. Metzler R, Jeon J H, Cherstvy A G, Barkai E. 2014. Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking. Phys. Chem. Chem. Phys., 16: 24128-24164.
[169]	Metzler R, Klafter J. 2000. The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep., 339: 1-77. Metzler R, Klafter J. 2000. The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep., 339: 1-77.
[170]	Metzler R. 2019. Brownian motion and beyond: first-passage, power spectrum, non-Gaussianity, and anomalous diffusion. J. Stat. Mech-Theory E, 2019: 114003. doi: 10.1088/1742-5468/ab4988 Metzler R. 2019. Brownian motion and beyond: first-passage, power spectrum, non-Gaussianity, and anomalous diffusion. J. Stat. Mech-Theory E, 2019: 114003. doi: 10.1088/1742-5468/ab4988
[171]	Meyvis T K L, De Smedt S C, Van Oostveldt P, Demeester J. 1999. Fluorescence recovery after photobleaching: a versatile tool for mobility and interaction measurements in pharmaceutical research. Pharm. Res., 16: 1153-1162. Meyvis T K L, De Smedt S C, Van Oostveldt P, Demeester J. 1999. Fluorescence recovery after photobleaching: a versatile tool for mobility and interaction measurements in pharmaceutical research. Pharm. Res., 16: 1153-1162.
[172]	Mignot T, Shaevitz J W. 2008. Active and passive mechanisms of intracellular transport and localization in bacteria. Curr. Opin. Microbiol., 11: 580-585. doi: 10.1016/j.mib.2008.10.005 Mignot T, Shaevitz J W. 2008. Active and passive mechanisms of intracellular transport and localization in bacteria. Curr. Opin. Microbiol., 11: 580-585. doi: 10.1016/j.mib.2008.10.005
[173]	Montroll E W, Weiss G H. 1965. Random walks on lattices. II. J. Math. Phys., 6: 167-181. Montroll E W, Weiss G H. 1965. Random walks on lattices. II. J. Math. Phys., 6: 167-181.
[174]	Moran J L, Posner J D. 2017. Phoretic self-propulsion. Annu. Rev. Fluid Mech., 49: 511-540. doi: 10.1103/PHYSREVE.109.014613 Moran J L, Posner J D. 2017. Phoretic self-propulsion. Annu. Rev. Fluid Mech., 49: 511-540. doi: 10.1103/PHYSREVE.109.014613
[175]	Morozov A, Marenduzzo D. 2014. Enhanced diffusion of tracer particles in dilute bacterial suspensions. Soft Matter, 10: 2748. Morozov A, Marenduzzo D. 2014. Enhanced diffusion of tracer particles in dilute bacterial suspensions. Soft Matter, 10: 2748.
[176]	Moschakis T. 2013. Microrheology and particle tracking in food gels and emulsions. Curr. Opin. Colloid In., 18: 311-323. Moschakis T. 2013. Microrheology and particle tracking in food gels and emulsions. Curr. Opin. Colloid In., 18: 311-323.
[177]	Muñoz Gil G, Bachimanchi H, Pineda J, Midtvedt B, Fernández Fernández G, Requena B, Ahsini Y, Asghar S, Bae J, Barrantes F J, Bender S W B, Cabriel C, Conejero J A, Escoto M, Feng X C, Haidari R, Hatzakis N S, Huang Z H, Izeddin I, Jeong H, Jiang Y, Kæstel Hansen J, Miné Hattab J, Ni R, Park J, Qu X, Saavedra L A, Sha H, Sokolovska N, Zhang Y B, Volpe Giorgio, Lewenstein M, Metzler R, Krapf D, Volpe Giovanni, Manzo C. 2025. Quantitative evaluation of methods to analyze motion changes in single-particle experiments. Nat. Commun., 16: 6749. doi: 10.1038/s41467-025-61949-x Muñoz Gil G, Bachimanchi H, Pineda J, Midtvedt B, Fernández Fernández G, Requena B, Ahsini Y, Asghar S, Bae J, Barrantes F J, Bender S W B, Cabriel C, Conejero J A, Escoto M, Feng X C, Haidari R, Hatzakis N S, Huang Z H, Izeddin I, Jeong H, Jiang Y, Kæstel Hansen J, Miné Hattab J, Ni R, Park J, Qu X, Saavedra L A, Sha H, Sokolovska N, Zhang Y B, Volpe Giorgio, Lewenstein M, Metzler R, Krapf D, Volpe Giovanni, Manzo C. 2025. Quantitative evaluation of methods to analyze motion changes in single-particle experiments. Nat. Commun., 16: 6749. doi: 10.1038/s41467-025-61949-x
[178]	Muñoz Gil G, Garcia March M A, Manzo C, Martín Guerrero J D, Lewenstein M. 2020. Single trajectory characterization via machine learning. New J. Phys., 22: 013010. Muñoz Gil G, Garcia March M A, Manzo C, Martín Guerrero J D, Lewenstein M. 2020. Single trajectory characterization via machine learning. New J. Phys., 22: 013010.
[179]	Muñoz Gil G, Volpe Giovanni, Garcia March M A, Aghion E, Argun A, Hong C B, Bland T, Bo S, Conejero J A, Firbas N, Garibo I Orts Ò, Gentili A, Huang Z H, Jeon J H, Kabbech H, Kim Y, Kowalek P, Krapf D, Loch Olszewska H, Lomholt M A, Masson J B, Meyer P G, Park S, Requena B, Smal I, Song T, Szwabiński J, Thapa S, Verdier H, Volpe Giorgio, Widera A, Lewenstein M, Metzler R, Manzo C. 2021. Objective comparison of methods to decode anomalous diffusion. Nat. Commun., 12: 6253. doi: 10.1038/s41467-021-26320-w Muñoz Gil G, Volpe Giovanni, Garcia March M A, Aghion E, Argun A, Hong C B, Bland T, Bo S, Conejero J A, Firbas N, Garibo I Orts Ò, Gentili A, Huang Z H, Jeon J H, Kabbech H, Kim Y, Kowalek P, Krapf D, Loch Olszewska H, Lomholt M A, Masson J B, Meyer P G, Park S, Requena B, Smal I, Song T, Szwabiński J, Thapa S, Verdier H, Volpe Giorgio, Widera A, Lewenstein M, Metzler R, Manzo C. 2021. Objective comparison of methods to decode anomalous diffusion. Nat. Commun., 12: 6253. doi: 10.1038/s41467-021-26320-w
[180]	Mura S, Nicolas J, Couvreur P. 2013. Stimuli-responsive nanocarriers for drug delivery. Nat. Mater., 12: 991-1003. Mura S, Nicolas J, Couvreur P. 2013. Stimuli-responsive nanocarriers for drug delivery. Nat. Mater., 12: 991-1003.
[181]	Nehme E, Weiss L E, Michaeli T, Shechtman Y. 2018. Deep-STORM: super-resolution single-molecule microscopy by deep learning. Optica, 5: 458-464. doi: 10.1364/OPTICA.5.000458 Nehme E, Weiss L E, Michaeli T, Shechtman Y. 2018. Deep-STORM: super-resolution single-molecule microscopy by deep learning. Optica, 5: 458-464. doi: 10.1364/OPTICA.5.000458
[182]	Nelson B J, Pané S. 2023. Delivering drugs with microrobots. Science, 382: 1120-1122. Nelson B J, Pané S. 2023. Delivering drugs with microrobots. Science, 382: 1120-1122.
[183]	Nishizawa K, Bremerich M, Ayade H, Schmidt C F, Ariga T, Mizuno D. 2017. Feedback-tracking microrheology in living cells. Sci. Adv., 3: e1700318. Nishizawa K, Bremerich M, Ayade H, Schmidt C F, Ariga T, Mizuno D. 2017. Feedback-tracking microrheology in living cells. Sci. Adv., 3: e1700318.
[184]	Norregaard K, Metzler R, Ritter C M, Berg-Sørensen K, Oddershede L B. 2017. Manipulation and motion of organelles and single molecules in living cells. Chem. Rev., 117: 4342-4375. doi: 10.1021/acs.chemrev.6b00638 Norregaard K, Metzler R, Ritter C M, Berg-Sørensen K, Oddershede L B. 2017. Manipulation and motion of organelles and single molecules in living cells. Chem. Rev., 117: 4342-4375. doi: 10.1021/acs.chemrev.6b00638
[185]	Ochab Marcinek A, Hołyst R. 2011. Scale-dependent diffusion of spheres in solutions of flexible and rigid polymers: mean square displacement and autocorrelation function for FCS and DLS measurements. Soft Matter, 7: 7366-7374. doi: 10.1039/c1sm05217a Ochab Marcinek A, Hołyst R. 2011. Scale-dependent diffusion of spheres in solutions of flexible and rigid polymers: mean square displacement and autocorrelation function for FCS and DLS measurements. Soft Matter, 7: 7366-7374. doi: 10.1039/c1sm05217a
[186]	Oleg K, Grégoire B. 2002. Fluorescence correlation spectroscopy: the technique and its applications. Rep. Prog. Phys., 65: 251. Oleg K, Grégoire B. 2002. Fluorescence correlation spectroscopy: the technique and its applications. Rep. Prog. Phys., 65: 251.
[187]	Palacci J, Sacanna S, Steinberg A P, Pine D J, Chaikin P M. 2013. Living crystals of light-activated colloidal surfers. Science, 339: 936-940. Palacci J, Sacanna S, Steinberg A P, Pine D J, Chaikin P M. 2013. Living crystals of light-activated colloidal surfers. Science, 339: 936-940.
[188]	Pankhurst Q A, Connolly J, Jones S K, Dobson J. 2003. Applications of magnetic nanoparticles in biomedicine. J. Phys. D: Appl. Phys., 36: R167. Pankhurst Q A, Connolly J, Jones S K, Dobson J. 2003. Applications of magnetic nanoparticles in biomedicine. J. Phys. D: Appl. Phys., 36: R167.
[189]	Park S, Thapa S, Kim Y, Lomholt M A, Jeon J H. 2021. Bayesian inference of lévy walks via hidden markov models. J. Phys. A-Math. Theor., 54: 484001. doi: 10.1088/1751-8121/ac31a1 Park S, Thapa S, Kim Y, Lomholt M A, Jeon J H. 2021. Bayesian inference of lévy walks via hidden markov models. J. Phys. A-Math. Theor., 54: 484001. doi: 10.1088/1751-8121/ac31a1
[190]	Pastore R, Ciarlo A, Pesce G, Greco F, Sasso A. 2021. Rapid fickian yet non-gaussian diffusion after subdiffusion. Phys. Rev. Lett., 126: 158003. doi: 10.1103/PhysRevLett.126.158003 Pastore R, Ciarlo A, Pesce G, Greco F, Sasso A. 2021. Rapid fickian yet non-gaussian diffusion after subdiffusion. Phys. Rev. Lett., 126: 158003. doi: 10.1103/PhysRevLett.126.158003
[191]	Pechukas P. 1967. Generalized langevin equation of mori and kubo. Phys. Rev., 164: 174-175. Pechukas P. 1967. Generalized langevin equation of mori and kubo. Phys. Rev., 164: 174-175.
[192]	Percus J K. 1974. Anomalous self-diffusion for one-dimensional hard cores. Phys. Rev. A, 9: 557-559. Percus J K. 1974. Anomalous self-diffusion for one-dimensional hard cores. Phys. Rev. A, 9: 557-559.
[193]	Peulen T O, Wilkinson, K J. 2011. Diffusion of nanoparticles in a biofilm. Environ. Sci. Technol., 45: 3367-3373. Peulen T O, Wilkinson, K J. 2011. Diffusion of nanoparticles in a biofilm. Environ. Sci. Technol., 45: 3367-3373.
[194]	Pineda J, Midtvedt B, Bachimanchi H, Noé S, Midtvedt D, Volpe G, Manzo C. 2023. Geometric deep learning reveals the spatiotemporal features of microscopic motion. Nat. Mach. Intell., 5: 71-82. doi: 10.1038/s42256-022-00595-0 Pineda J, Midtvedt B, Bachimanchi H, Noé S, Midtvedt D, Volpe G, Manzo C. 2023. Geometric deep learning reveals the spatiotemporal features of microscopic motion. Nat. Mach. Intell., 5: 71-82. doi: 10.1038/s42256-022-00595-0
[195]	Pinholt H D, Bohr S S R, Iversen J F, Boomsma W, Hatzakis N S. 2021. Single-particle diffusional fingerprinting: a machine-learning framework for quantitative analysis of heterogeneous diffusion. Proc. Natl. Acad. Sci. U. S. A., 118: e2104624118. Pinholt H D, Bohr S S R, Iversen J F, Boomsma W, Hatzakis N S. 2021. Single-particle diffusional fingerprinting: a machine-learning framework for quantitative analysis of heterogeneous diffusion. Proc. Natl. Acad. Sci. U. S. A., 118: e2104624118.
[196]	Piskorz T K, Ochab Marcinek A. 2014. A universal model of restricted diffusion for fluorescence correlation spectroscopy. J. Phys. Chem. B, 118: 4906-4912. Piskorz T K, Ochab Marcinek A. 2014. A universal model of restricted diffusion for fluorescence correlation spectroscopy. J. Phys. Chem. B, 118: 4906-4912.
[197]	Pronk S, Lindahl E, Kasson P M. 2014. Dynamic heterogeneity controls diffusion and viscosity near biological interfaces. Nat. Commun., 5: 3034. Pronk S, Lindahl E, Kasson P M. 2014. Dynamic heterogeneity controls diffusion and viscosity near biological interfaces. Nat. Commun., 5: 3034.
[198]	Qu H C, Yang Y, Cui Z C, Wang D, Xue C D, Qin K R. 2023. Temperature‐mediated diffusion of nanoparticles in semidilute polymer solutions. Electrophoresis, 44: 1899-1906. Qu H C, Yang Y, Cui Z C, Wang D, Xue C D, Qin K R. 2023. Temperature‐mediated diffusion of nanoparticles in semidilute polymer solutions. Electrophoresis, 44: 1899-1906.
[199]	Qu X, Hu Y, Cai W J, Xu Y, Ke H, Zhu G L, Huang Z H. 2024. Semantic segmentation of anomalous diffusion using deep convolutional networks. Phys. Rev. Research, 6: 013054. Qu X, Hu Y, Cai W J, Xu Y, Ke H, Zhu G L, Huang Z H. 2024. Semantic segmentation of anomalous diffusion using deep convolutional networks. Phys. Rev. Research, 6: 013054.
[200]	R Kubo. 1966. The fluctuation-dissipation theorem. Rep. Prog. Phys., 29: 255. R Kubo. 1966. The fluctuation-dissipation theorem. Rep. Prog. Phys., 29: 255.
[201]	Ren Y T, Chen Q, He M J, Zhang X Z, Qi H, Yan Y Y. 2021. Plasmonic optical tweezers for particle manipulation: principles, methods, and applications. ACS Nano, 15: 6105-6128. doi: 10.1021/acsnano.1c00466 Ren Y T, Chen Q, He M J, Zhang X Z, Qi H, Yan Y Y. 2021. Plasmonic optical tweezers for particle manipulation: principles, methods, and applications. ACS Nano, 15: 6105-6128. doi: 10.1021/acsnano.1c00466
[202]	Requena B, Masó S, Bertran J, Lewenstein M, Manzo C, Muñoz Gil G. 2023. Inferring pointwise diffusion properties of single trajectories with deep learning. Biophys. J., 122: 4360-4369. Requena B, Masó S, Bertran J, Lewenstein M, Manzo C, Muñoz Gil G. 2023. Inferring pointwise diffusion properties of single trajectories with deep learning. Biophys. J., 122: 4360-4369.
[203]	Reverey J F, Jeon J H, Bao H, Leippe M, Metzler R, Selhuber-Unkel C. 2015. Superdiffusion dominates intracellular particle motion in the supercrowded cytoplasm of pathogenic acanthamoeba castellanii. Sci. Rep., 5: 11690. Reverey J F, Jeon J H, Bao H, Leippe M, Metzler R, Selhuber-Unkel C. 2015. Superdiffusion dominates intracellular particle motion in the supercrowded cytoplasm of pathogenic acanthamoeba castellanii. Sci. Rep., 5: 11690.
[204]	Reyes-Ortega F. 2014. Smart polymers and their applications. Woodhead Publishing. Reyes-Ortega F. 2014. Smart polymers and their applications. Woodhead Publishing.
[205]	Reynolds A M, Rhodes C J. 2009. The lévy flight paradigm: random search patterns and mechanisms. Ecology, 90: 877-887. Reynolds A M, Rhodes C J. 2009. The lévy flight paradigm: random search patterns and mechanisms. Ecology, 90: 877-887.
[206]	Richardson L F. 1926. Atmospheric diffusion shown on a distance-neighbour graph. Proc. R. Soc. Lond. A, 110: 709-737. Richardson L F. 1926. Atmospheric diffusion shown on a distance-neighbour graph. Proc. R. Soc. Lond. A, 110: 709-737.
[207]	Romanczuk P, Bär M, Ebeling W, Lindner B, Schimansky-Geier L. 2012. Active brownian particles: from individual to collective stochastic dynamics. Eur. Phys. J. Spec. Top., 202: 1-162. Romanczuk P, Bär M, Ebeling W, Lindner B, Schimansky-Geier L. 2012. Active brownian particles: from individual to collective stochastic dynamics. Eur. Phys. J. Spec. Top., 202: 1-162.
[208]	Russo A, Durán-Olivencia M A, Kevrekidis I G, Kalliadasis S. 2024. Machine learning memory kernels as closure for non-markovian stochastic processes. IEEE Trans. Neural Netw. Learning Syst., 35: 6531-6543. doi: 10.1109/TNNLS.2022.3210695 Russo A, Durán-Olivencia M A, Kevrekidis I G, Kalliadasis S. 2024. Machine learning memory kernels as closure for non-markovian stochastic processes. IEEE Trans. Neural Netw. Learning Syst., 35: 6531-6543. doi: 10.1109/TNNLS.2022.3210695
[209]	S Mogre S, Brown A I, Koslover E F. 2020. Getting around the cell: physical transport in the intracellular world. Phys. Biol., 17: 061003. doi: 10.1088/1478-3975/aba5e5 S Mogre S, Brown A I, Koslover E F. 2020. Getting around the cell: physical transport in the intracellular world. Phys. Biol., 17: 061003. doi: 10.1088/1478-3975/aba5e5
[210]	Sabri A, Xu X R, Krapf D, Weiss M. 2020. Elucidating the origin of heterogeneous anomalous diffusion in the cytoplasm of mammalian cells. Phys. Rev. Lett., 125: 058101. doi: 10.1103/PhysRevLett.125.058101 Sabri A, Xu X R, Krapf D, Weiss M. 2020. Elucidating the origin of heterogeneous anomalous diffusion in the cytoplasm of mammalian cells. Phys. Rev. Lett., 125: 058101. doi: 10.1103/PhysRevLett.125.058101
[211]	Safdar M, Khan S U, Jänis J. 2018. Progress toward catalytic micro- and nanomotors for biomedical and environmental applications. Adv. Mater., 30: 1703660. Safdar M, Khan S U, Jänis J. 2018. Progress toward catalytic micro- and nanomotors for biomedical and environmental applications. Adv. Mater., 30: 1703660.
[212]	Sakamoto K, Akimoto T, Muramatsu M, Sansom M S P, Metzler R, Yamamoto E. 2023. Heterogeneous biological membranes regulate protein partitioning via fluctuating diffusivity. PNAS Nexus., 2: pgad258. doi: 10.1093/PNASNEXUS/PGAD258 Sakamoto K, Akimoto T, Muramatsu M, Sansom M S P, Metzler R, Yamamoto E. 2023. Heterogeneous biological membranes regulate protein partitioning via fluctuating diffusivity. PNAS Nexus., 2: pgad258. doi: 10.1093/PNASNEXUS/PGAD258
[213]	Sakaue T, Saito T. 2016. Active diffusion of model chromosomal loci driven by athermal noise. Soft Matter, 13: 81-87. Sakaue T, Saito T. 2016. Active diffusion of model chromosomal loci driven by athermal noise. Soft Matter, 13: 81-87.
[214]	Saltzman E J, Schweizer K S. 2008. Large-amplitude jumps and non-gaussian dynamics in highly concentrated hard sphere fluids. Phys. Rev. E, 77: 051504. Saltzman E J, Schweizer K S. 2008. Large-amplitude jumps and non-gaussian dynamics in highly concentrated hard sphere fluids. Phys. Rev. E, 77: 051504.
[215]	Samanta N, Chakrabarti R. 2016. Tracer diffusion in a sea of polymers with binding zones: mobile vs. frozen traps. Soft Matter, 12: 8554-8563. Samanta N, Chakrabarti R. 2016. Tracer diffusion in a sea of polymers with binding zones: mobile vs. frozen traps. Soft Matter, 12: 8554-8563.
[216]	Sandev T, Metzler R, Chechkin A. 2018. From continuous time random walks to the generalized diffusion equation. Fract. Calc. Appl. Anal., 21: 10-28. Sandev T, Metzler R, Chechkin A. 2018. From continuous time random walks to the generalized diffusion equation. Fract. Calc. Appl. Anal., 21: 10-28.
[217]	Sarmiento Gomez E, Santamaria Holek I, Castillo R. 2014. Mean-square displacement of particles in slightly interconnected polymer networks. J Phys. Chem. B, 118: 1146-1158. Sarmiento Gomez E, Santamaria Holek I, Castillo R. 2014. Mean-square displacement of particles in slightly interconnected polymer networks. J Phys. Chem. B, 118: 1146-1158.
[218]	Sawford B. 2001. Turbulent relative dispersion. Annu. Rev. Fluid Mech., 33: 289-317. Sawford B. 2001. Turbulent relative dispersion. Annu. Rev. Fluid Mech., 33: 289-317.
[219]	Saxton M J. 1994. Anomalous diffusion due to obstacles: a monte carlo study. Biophys. J., 66: 394-401. Saxton M J. 1994. Anomalous diffusion due to obstacles: a monte carlo study. Biophys. J., 66: 394-401.
[220]	Saxton M J. 1996. Anomalous diffusion due to binding: a monte carlo study. Biophys. J., 70: 1250-1262. Saxton M J. 1996. Anomalous diffusion due to binding: a monte carlo study. Biophys. J., 70: 1250-1262.
[221]	Saxton M J. 2007. A biological interpretation of transient anomalous subdiffusion. I. qualitative model. Biophys. J., 92: 1178-1191. Saxton M J. 2007. A biological interpretation of transient anomalous subdiffusion. I. qualitative model. Biophys. J., 92: 1178-1191.
[222]	Saxton M J. 2008. Single-particle tracking: connecting the dots. Nat. Methods, 5: 671-672. doi: 10.1038/nmeth0808-671 Saxton M J. 2008. Single-particle tracking: connecting the dots. Nat. Methods, 5: 671-672. doi: 10.1038/nmeth0808-671
[223]	Schimek N, Wood T R, Beck D A C, McKenna M, Toghani A, Nance E. 2024. High-fidelity predictions of diffusion in the brain microenvironment. Biophys. J., 123: 3935-3950. Schimek N, Wood T R, Beck D A C, McKenna M, Toghani A, Nance E. 2024. High-fidelity predictions of diffusion in the brain microenvironment. Biophys. J., 123: 3935-3950.
[224]	Schütz G J, Schindler H, Schmidt T. 1997. Single-molecule microscopy on model membranes reveals anomalous diffusion. Biophys. J., 73: 1073-1080. Schütz G J, Schindler H, Schmidt T. 1997. Single-molecule microscopy on model membranes reveals anomalous diffusion. Biophys. J., 73: 1073-1080.
[225]	Schweitzer F, Ebeling W, Tilch B. 1998. Complex motion of brownian particles with energy depots. Phys. Rev. Lett., 80: 5044-5047. Schweitzer F, Ebeling W, Tilch B. 1998. Complex motion of brownian particles with energy depots. Phys. Rev. Lett., 80: 5044-5047.
[226]	Seckler H, Metzler R. 2022. Bayesian deep learning for error estimation in the analysis of anomalous diffusion. Nat. Commun., 13: 6717. Seckler H, Metzler R. 2022. Bayesian deep learning for error estimation in the analysis of anomalous diffusion. Nat. Commun., 13: 6717.
[227]	Shaban H A, Seeber A. 2020. Monitoring the spatio-temporal organization and dynamics of the genome. Nucleic Acids Res., 48: 3423-3434. Shaban H A, Seeber A. 2020. Monitoring the spatio-temporal organization and dynamics of the genome. Nucleic Acids Res., 48: 3423-3434.
[228]	Shabeeb Z, Goyal N, Attah Nantogmah P, Jamali V. 2025. Learning the diffusion of nanoparticles in liquid phase TEM via physics-informed generative AI. Nat. Commun., 16: 6298. Shabeeb Z, Goyal N, Attah Nantogmah P, Jamali V. 2025. Learning the diffusion of nanoparticles in liquid phase TEM via physics-informed generative AI. Nat. Commun., 16: 6298.
[229]	Shen H, Tauzin L J, Baiyasi R, Wang W X, Moringo N, Shuang B, Landes C F. 2017. Single particle tracking: from theory to biophysical applications. Chem. Rev., 117: 7331-7376. Shen H, Tauzin L J, Baiyasi R, Wang W X, Moringo N, Shuang B, Landes C F. 2017. Single particle tracking: from theory to biophysical applications. Chem. Rev., 117: 7331-7376.
[230]	Singh D, Singh L. 2025. A pioneering review on quantitative analysis of the effect of macromolecular crowding on drug transport and release: current implications. J. Macromol. Sci. B, 64: 902-916. Singh D, Singh L. 2025. A pioneering review on quantitative analysis of the effect of macromolecular crowding on drug transport and release: current implications. J. Macromol. Sci. B, 64: 902-916.
[231]	Skaug M J, Wang L, Ding Y F, Schwartz D K. 2015. Hindered nanoparticle diffusion and void accessibility in a three-dimensional porous medium. ACS Nano, 9: 2148-2156. doi: 10.1021/acsnano.5b00019 Skaug M J, Wang L, Ding Y F, Schwartz D K. 2015. Hindered nanoparticle diffusion and void accessibility in a three-dimensional porous medium. ACS Nano, 9: 2148-2156. doi: 10.1021/acsnano.5b00019
[232]	Song D L, Zhang X, Li B Y, Sun Y F, Mei H H, Cheng X J, Li J M, Cheng X D, Fang N. 2024. Deep learning-assisted automated multidimensional single particle tracking in living cells. Nano Lett., 24: 3082-3088. Song D L, Zhang X, Li B Y, Sun Y F, Mei H H, Cheng X J, Li J M, Cheng X D, Fang N. 2024. Deep learning-assisted automated multidimensional single particle tracking in living cells. Nano Lett., 24: 3082-3088.
[233]	Soula H, Care B, Beslon G, Berry H. 2013. Anomalous versus slowed-down brownian diffusion in the ligand-binding equilibrium. Biophys. J., 105: 2064-2073. Soula H, Care B, Beslon G, Berry H. 2013. Anomalous versus slowed-down brownian diffusion in the ligand-binding equilibrium. Biophys. J., 105: 2064-2073.
[234]	Sposini V, Chechkin A, Seno F, Pagnini G, Metzler R, 2018. Random diffusivity from stochastic equations: comparison of two models for brownian yet non-gaussian diffusion. New J. Phys. , 20: 043044. Sposini V, Chechkin A, Seno F, Pagnini G, Metzler R, 2018. Random diffusivity from stochastic equations: comparison of two models for brownian yet non-gaussian diffusion. New J. Phys. , 20: 043044.
[235]	Sposini V, Krapf D, Marinari E, Sunyer R, Ritort F, Taheri F, Selhuber-Unkel C, Benelli R, Weiss M, Metzler R, Oshanin G. 2022. Towards a robust criterion of anomalous diffusion. Commun. Phys., 5: 305. doi: 10.1038/S42005-022-01079-8 Sposini V, Krapf D, Marinari E, Sunyer R, Ritort F, Taheri F, Selhuber-Unkel C, Benelli R, Weiss M, Metzler R, Oshanin G. 2022. Towards a robust criterion of anomalous diffusion. Commun. Phys., 5: 305. doi: 10.1038/S42005-022-01079-8
[236]	Sprakel J, van der Gucht J, Cohen Stuart M A, Besseling N A. 2008. Brownian particles in transient polymer networks. Phys. Rev. E, 77: 061502. Sprakel J, van der Gucht J, Cohen Stuart M A, Besseling N A. 2008. Brownian particles in transient polymer networks. Phys. Rev. E, 77: 061502.
[237]	Squires T M, Bazant M Z. 2004. Induced-charge electro-osmosis. J. Fluid Mech., 509: 217-252. Squires T M, Bazant M Z. 2004. Induced-charge electro-osmosis. J. Fluid Mech., 509: 217-252.
[238]	Squires T M, Mason T G. 2010. Fluid mechanics of microrheology. Annu. Rev. Fluid Mech., 42: 413-438. doi: 10.1146/annurev-fluid-121108-145608 Squires T M, Mason T G. 2010. Fluid mechanics of microrheology. Annu. Rev. Fluid Mech., 42: 413-438. doi: 10.1146/annurev-fluid-121108-145608
[239]	Squires T M, Mason T G. 2010. Fluid mechanics of microrheology. Annu. Rev. Fluid Mech., 42: 413-438. doi: 10.1146/annurev-fluid-121108-145608 Squires T M, Mason T G. 2010. Fluid mechanics of microrheology. Annu. Rev. Fluid Mech., 42: 413-438. doi: 10.1146/annurev-fluid-121108-145608
[240]	Stempfle B, Große A, Ferse B, Arndt K F, Wöll D. 2014. Anomalous diffusion in thermoresponsive polymer–clay composite hydrogels probed by wide-field fluorescence microscopy. Langmuir, 30: 14056-14061. Stempfle B, Große A, Ferse B, Arndt K F, Wöll D. 2014. Anomalous diffusion in thermoresponsive polymer–clay composite hydrogels probed by wide-field fluorescence microscopy. Langmuir, 30: 14056-14061.
[241]	Stoop R L, Straube A V, Tierno P. 2019. Enhancing nanoparticle diffusion on a unidirectional domain wall magnetic ratchet. Nano Lett., 19: 433-440. Stoop R L, Straube A V, Tierno P. 2019. Enhancing nanoparticle diffusion on a unidirectional domain wall magnetic ratchet. Nano Lett., 19: 433-440.
[242]	Sun S W, Zhang K, Xu S, Shi X H, Wang J L. , 2025. Diffusion of nanosheets in unentangled polymer melts. ACS Macro Lett. , 14: 284–291. Sun S W, Zhang K, Xu S, Shi X H, Wang J L. , 2025. Diffusion of nanosheets in unentangled polymer melts. ACS Macro Lett. , 14: 284–291.
[243]	Szymanski J, Weiss M. 2009. Elucidating the origin of anomalous diffusion in crowded fluids. Phys. Rev. Lett., 103: 038102. Szymanski J, Weiss M. 2009. Elucidating the origin of anomalous diffusion in crowded fluids. Phys. Rev. Lett., 103: 038102.
[244]	Tsallis C, Levy S V, Souza A M, Maynard R. 1995. Statistical-mechanical foundation of the ubiquity of lévy distributions in Nature. Phys. Rev. Lett., 75: 3589-3593. Tsallis C, Levy S V, Souza A M, Maynard R. 1995. Statistical-mechanical foundation of the ubiquity of lévy distributions in Nature. Phys. Rev. Lett., 75: 3589-3593.
[245]	Tuteja A, Mackay M E, Narayanan S, Asokan S, Wong M S. 2007. Breakdown of the continuum stokes−einstein relation for nanoparticle diffusion. Nano Lett., 7: 1276-1281. Tuteja A, Mackay M E, Narayanan S, Asokan S, Wong M S. 2007. Breakdown of the continuum stokes−einstein relation for nanoparticle diffusion. Nano Lett., 7: 1276-1281.
[246]	Uhlenbeck G E, Ornstein L S. 1930. On the theory of the brownian motion. Phys. Rev., 36: 823-841. Uhlenbeck G E, Ornstein L S. 1930. On the theory of the brownian motion. Phys. Rev., 36: 823-841.
[247]	Ussia M, Urso M, Kment S, Fialova T, Klima K, Dolezelikova K, Pumera M. 2022. Light‐propelled nanorobots for facial titanium implants biofilms removal. Small, 18: 2200708. Ussia M, Urso M, Kment S, Fialova T, Klima K, Dolezelikova K, Pumera M. 2022. Light‐propelled nanorobots for facial titanium implants biofilms removal. Small, 18: 2200708.
[248]	Vagias A, Raccis R, Koynov K, Jonas U, Butt H J, Fytas G, Kosovan P, Lenz O, Holm C. 2013. Complex tracer diffusion dynamics in polymer solutions. Phys. Rev. Lett., 111: 088301. Vagias A, Raccis R, Koynov K, Jonas U, Butt H J, Fytas G, Kosovan P, Lenz O, Holm C. 2013. Complex tracer diffusion dynamics in polymer solutions. Phys. Rev. Lett., 111: 088301.
[249]	Van Zanten J H, Amin S, Abdala A A. 2004. Brownian motion of colloidal spheres in aqueous PEO solutions. Macromolecules, 37: 3874-3880. Van Zanten J H, Amin S, Abdala A A. 2004. Brownian motion of colloidal spheres in aqueous PEO solutions. Macromolecules, 37: 3874-3880.
[250]	Veiseh O, Gunn J W, Zhang M Q. 2010. Design and fabrication of magnetic nanoparticles for targeted drug delivery and imaging. Adv. Drug Delivery Rev., 62: 284-304. Veiseh O, Gunn J W, Zhang M Q. 2010. Design and fabrication of magnetic nanoparticles for targeted drug delivery and imaging. Adv. Drug Delivery Rev., 62: 284-304.
[251]	Vilk O, Aghion E, Avgar T, Beta C, Nagel O, Sabri A, Sarfati R, Schwartz D K, Weiss M, Krapf D, Nathan R, Metzler R, Assaf M. 2022. Unravelling the origins of anomalous diffusion: From molecules to migrating storks. Phys. Rev. Research, 4: 033055. Vilk O, Aghion E, Avgar T, Beta C, Nagel O, Sabri A, Sarfati R, Schwartz D K, Weiss M, Krapf D, Nathan R, Metzler R, Assaf M. 2022. Unravelling the origins of anomalous diffusion: From molecules to migrating storks. Phys. Rev. Research, 4: 033055.
[252]	Volgin I V, Larin S V, Abad E, Lyulin S V. 2017. Molecular dynamics simulations of fullerene diffusion in polymer melts. Macromolecules, 50: 2207-2218. Volgin I V, Larin S V, Abad E, Lyulin S V. 2017. Molecular dynamics simulations of fullerene diffusion in polymer melts. Macromolecules, 50: 2207-2218.
[253]	von Smoluchowski M. 1906. Zur kinetischen Theorie der brownschen molekularbewegung und der suspensionen. Ann. Phys., 326: 756-780. von Smoluchowski M. 1906. Zur kinetischen Theorie der brownschen molekularbewegung und der suspensionen. Ann. Phys., 326: 756-780.
[254]	Wachsmuth M, Waldeck W, Langowski J. 2000. Anomalous diffusion of fluorescent probes inside living cell nuclei investigated by spatially-resolved fluorescence correlation spectroscopy. J. Mol. Biol., 298: 677-689. Wachsmuth M, Waldeck W, Langowski J. 2000. Anomalous diffusion of fluorescent probes inside living cell nuclei investigated by spatially-resolved fluorescence correlation spectroscopy. J. Mol. Biol., 298: 677-689.
[255]	Wagner T, Kroll A, Haramagatti C R, Lipinski H G, Wiemann M. 2017. Classification and segmentation of nanoparticle diffusion trajectories in cellular micro environments. PLoS One, 12: e0170165. Wagner T, Kroll A, Haramagatti C R, Lipinski H G, Wiemann M. 2017. Classification and segmentation of nanoparticle diffusion trajectories in cellular micro environments. PLoS One, 12: e0170165.
[256]	Waigh T A, Korabel N. 2023. Heterogeneous anomalous transport in cellular and molecular biology. Rep. Prog. Phys., 86: 126601. Waigh T A, Korabel N. 2023. Heterogeneous anomalous transport in cellular and molecular biology. Rep. Prog. Phys., 86: 126601.
[257]	Wang B, Anthony S M, Bae S C, Granick S. 2009. Anomalous yet brownian. Proc. Natl. Acad. Sci. U. S. A., 106: 15160-15164. doi: 10.1088/1361-6633/AE358C Wang B, Anthony S M, Bae S C, Granick S. 2009. Anomalous yet brownian. Proc. Natl. Acad. Sci. U. S. A., 106: 15160-15164. doi: 10.1088/1361-6633/AE358C
[258]	Wang B, Anthony S M, Bae S C, Granick S. 2009. Anomalous yet brownian. Proc. Natl. Acad. Sci. U. S. A., 106: 15160-15164. Wang B, Anthony S M, Bae S C, Granick S. 2009. Anomalous yet brownian. Proc. Natl. Acad. Sci. U. S. A., 106: 15160-15164.
[259]	Wang B, Kuo J, Bae S C, Granick S. 2012. When brownian diffusion is not gaussian. Nat. Mater., 11: 481-485. Wang B, Kuo J, Bae S C, Granick S. 2012. When brownian diffusion is not gaussian. Nat. Mater., 11: 481-485.
[260]	Wang B, Kuo J, Granick S. 2013. Bursts of active transport in living cells. Phys. Rev. Lett., 111: 208102. Wang B, Kuo J, Granick S. 2013. Bursts of active transport in living cells. Phys. Rev. Lett., 111: 208102.
[261]	Wang D P, He C L, Stoykovich M P, Schwartz D K. 2015. Nanoscale topography influences polymer surface diffusion. ACS Nano, 9: 1656-1664. Wang D P, He C L, Stoykovich M P, Schwartz D K. 2015. Nanoscale topography influences polymer surface diffusion. ACS Nano, 9: 1656-1664.
[262]	Wang J L, Yang Y W, Yu M R, Hu G Q, Gan Y, Gao H J, Shi X H. 2018. Diffusion of rod-like nanoparticles in non-adhesive and adhesive porous polymeric gels. J. Mech. Phys. Solids, 112: 431-457. doi: 10.1016/j.jmps.2017.12.014 Wang J L, Yang Y W, Yu M R, Hu G Q, Gan Y, Gao H J, Shi X H. 2018. Diffusion of rod-like nanoparticles in non-adhesive and adhesive porous polymeric gels. J. Mech. Phys. Solids, 112: 431-457. doi: 10.1016/j.jmps.2017.12.014
[263]	Wang W, Cherstvy A G, Chechkin A V, Thapa S, Seno F, Liu X B, Metzler R. 2020. Fractional brownian motion with random diffusivity: emerging residual nonergodicity below the correlation time. J. Phys. A-Math. Theor., 53: 474001. doi: 10.1088/1751-8121/aba467 Wang W, Cherstvy A G, Chechkin A V, Thapa S, Seno F, Liu X B, Metzler R. 2020. Fractional brownian motion with random diffusivity: emerging residual nonergodicity below the correlation time. J. Phys. A-Math. Theor., 53: 474001. doi: 10.1088/1751-8121/aba467
[264]	Wang Z C, Yu H P, Liyanage A, Qiu J J, Thushara D, Bao B, Zhao S L. 2022. Collective diffusion of charged nanoparticles in microchannel under electric field. Chem. Eng. Sci., 248: 117264. doi: 10.1016/j.ces.2021.117264 Wang Z C, Yu H P, Liyanage A, Qiu J J, Thushara D, Bao B, Zhao S L. 2022. Collective diffusion of charged nanoparticles in microchannel under electric field. Chem. Eng. Sci., 248: 117264. doi: 10.1016/j.ces.2021.117264
[265]	Weber S C, Spakowitz A J, Theriot J A, 2010. Bacterial chromosomal loci move subdiffusively through a viscoelastic cytoplasm. Phys. Rev. Lett. , 104: 238102. Weber S C, Spakowitz A J, Theriot J A, 2010. Bacterial chromosomal loci move subdiffusively through a viscoelastic cytoplasm. Phys. Rev. Lett. , 104: 238102.
[266]	Weeks E R, Crocker J C, Levitt A C, Schofield A, Weitz D A. 2000. Three-dimensional direct imaging of structural relaxation near the colloidal glass transition. Science, 287: 627-631. doi: 10.1126/science.287.5453.627 Weeks E R, Crocker J C, Levitt A C, Schofield A, Weitz D A. 2000. Three-dimensional direct imaging of structural relaxation near the colloidal glass transition. Science, 287: 627-631. doi: 10.1126/science.287.5453.627
[267]	Wei Y R, Zhao M, He T P, Chen N, Rao L, Chen L, Zhang Y, Yang Y B, Yuan Q. 2023. Quantitatively lighting up the spatial organization of CD47/SIRPα immune checkpoints on the cellular membrane with single-molecule localization microscopy. ACS Nano, 17: 21626-21638. doi: 10.1021/ACSNANO.3C06709 Wei Y R, Zhao M, He T P, Chen N, Rao L, Chen L, Zhang Y, Yang Y B, Yuan Q. 2023. Quantitatively lighting up the spatial organization of CD47/SIRPα immune checkpoints on the cellular membrane with single-molecule localization microscopy. ACS Nano, 17: 21626-21638. doi: 10.1021/ACSNANO.3C06709
[268]	Weigel A V, Ragi S, Reid M L, Chong E K, Tamkun M M, Krapf D. 2012. Obstructed diffusion propagator analysis for single-particle tracking. Phys. Rev. E, 85: 041924. Weigel A V, Ragi S, Reid M L, Chong E K, Tamkun M M, Krapf D. 2012. Obstructed diffusion propagator analysis for single-particle tracking. Phys. Rev. E, 85: 041924.
[269]	Weigel A V, Simon B, Tamkun M M, Krapf D. 2011. Ergodic and nonergodic processes coexist in the plasma membrane as observed by single-molecule tracking. Proc. Natl. Acad. Sci. U. S. A., 108: 6438-6443. Weigel A V, Simon B, Tamkun M M, Krapf D. 2011. Ergodic and nonergodic processes coexist in the plasma membrane as observed by single-molecule tracking. Proc. Natl. Acad. Sci. U. S. A., 108: 6438-6443.
[270]	Weiss M, Elsner M, Kartberg F, Nilsson T. 2004. Anomalous subdiffusion is a measure for cytoplasmic crowding in living cells. Biophys. J., 87: 3518-3524. doi: 10.1529/biophysj.104.044263 Weiss M, Elsner M, Kartberg F, Nilsson T. 2004. Anomalous subdiffusion is a measure for cytoplasmic crowding in living cells. Biophys. J., 87: 3518-3524. doi: 10.1529/biophysj.104.044263
[271]	Weiss M, Hashimoto H, Nilsson T. 2003. Anomalous protein diffusion in living cells as seen by fluorescence correlation spectroscopy. Biophys. J., 84: 4043-4052. Weiss M, Hashimoto H, Nilsson T. 2003. Anomalous protein diffusion in living cells as seen by fluorescence correlation spectroscopy. Biophys. J., 84: 4043-4052.
[272]	Welsher K, Yang H. 2014. Multi-resolution 3D visualization of the early stages of cellular uptake of peptide-coated nanoparticles. Nat. Nanotech., 9: 198-203. doi: 10.1038/NNANO.2014.12 Welsher K, Yang H. 2014. Multi-resolution 3D visualization of the early stages of cellular uptake of peptide-coated nanoparticles. Nat. Nanotech., 9: 198-203. doi: 10.1038/NNANO.2014.12
[273]	Wensink H H, Dunkel J, Heidenreich S, Drescher K, Goldstein R E, Löwen H, Yeomans J M. 2012. Meso-scale turbulence in living fluids. Proc. Natl. Acad. Sci. U. S. A., 109: 14308-14313. doi: 10.1073/pnas.1202032109 Wensink H H, Dunkel J, Heidenreich S, Drescher K, Goldstein R E, Löwen H, Yeomans J M. 2012. Meso-scale turbulence in living fluids. Proc. Natl. Acad. Sci. U. S. A., 109: 14308-14313. doi: 10.1073/pnas.1202032109
[274]	Winkler R G, Elgeti J, Gompper G. 2017. Active polymers-emergent conformational and dynamical properties: a brief review. J. Phys. Soc. Jpn., 86: 101014. Winkler R G, Elgeti J, Gompper G. 2017. Active polymers-emergent conformational and dynamical properties: a brief review. J. Phys. Soc. Jpn., 86: 101014.
[275]	Wirtz D. 2009. Particle-tracking microrheology of living cells: principles and applications. Annu. Rev. Biophys., 38: 301-326. doi: 10.1146/annurev.biophys.050708.133724 Wirtz D. 2009. Particle-tracking microrheology of living cells: principles and applications. Annu. Rev. Biophys., 38: 301-326. doi: 10.1146/annurev.biophys.050708.133724
[276]	Witzel P, Götz M, Lanoiselée Y, Franosch T, Grebenkov D S, Heinrich D. 2019. Heterogeneities shape passive intracellular transport. Biophys. J., 117: 203-213. doi: 10.1016/j.bpj.2019.06.009 Witzel P, Götz M, Lanoiselée Y, Franosch T, Grebenkov D S, Heinrich D. 2019. Heterogeneities shape passive intracellular transport. Biophys. J., 117: 203-213. doi: 10.1016/j.bpj.2019.06.009
[277]	Woodhouse F G, Goldstein R E. 2013. Cytoplasmic streaming in plant cells emerges naturally by microfilament self-organization. Proc. Natl. Acad. Sci. U. S. A., 110: 14132-14137. Woodhouse F G, Goldstein R E. 2013. Cytoplasmic streaming in plant cells emerges naturally by microfilament self-organization. Proc. Natl. Acad. Sci. U. S. A., 110: 14132-14137.
[278]	Woringer M, Izeddin I, Favard C, Berry H. 2020. Anomalous subdiffusion in living cells: bridging the gap between experiments and realistic models through collaborative challenges. Front. Phys., 8: 134. Woringer M, Izeddin I, Favard C, Berry H. 2020. Anomalous subdiffusion in living cells: bridging the gap between experiments and realistic models through collaborative challenges. Front. Phys., 8: 134.
[279]	Wu X L, Libchaber A. 2000. Particle diffusion in a quasi-two-dimensional bacterial bath. Phys. Rev. Lett., 84: 3017-3020. Wu X L, Libchaber A. 2000. Particle diffusion in a quasi-two-dimensional bacterial bath. Phys. Rev. Lett., 84: 3017-3020.
[280]	Würger A. 2010. Thermal non-equilibrium transport in colloids. Rep. Prog. Phys., 73: 126601. doi: 10.1088/0034-4885/73/12/126601 Würger A. 2010. Thermal non-equilibrium transport in colloids. Rep. Prog. Phys., 73: 126601. doi: 10.1088/0034-4885/73/12/126601
[281]	Xiao B, Zheng X, Yu M R, Li H W, Jiang X H, Zhang L Y, Gong Y L, Cheng P, Xu H L, Lei X Q, Ding B W, Tian F L, Gan Y, Gao H J, Shi X H. 2026. Enhanced nanoparticle diffusion via deformation-driven network remodeling in cyclically stretched hydrogels. Nano Today, 69: 103037. Xiao B, Zheng X, Yu M R, Li H W, Jiang X H, Zhang L Y, Gong Y L, Cheng P, Xu H L, Lei X Q, Ding B W, Tian F L, Gan Y, Gao H J, Shi X H. 2026. Enhanced nanoparticle diffusion via deformation-driven network remodeling in cyclically stretched hydrogels. Nano Today, 69: 103037.
[282]	Xie C L, Liu Y N, Luo H, Jing G Y. 2022. Activity-induced enhancement of superdiffusive transport in bacterial turbulence. Micromachines, 13: 746. Xie C L, Liu Y N, Luo H, Jing G Y. 2022. Activity-induced enhancement of superdiffusive transport in bacterial turbulence. Micromachines, 13: 746.
[283]	Xu C, Yang K, Yuan B. 2023. Non-gaussian diffusion of individual lipids unveils the unique peptide–membrane interaction dynamics. J. Phys. Chem. Lett., 14: 854-862. Xu C, Yang K, Yuan B. 2023. Non-gaussian diffusion of individual lipids unveils the unique peptide–membrane interaction dynamics. J. Phys. Chem. Lett., 14: 854-862.
[284]	Xu Z Y, Dai X B, Bu X Y, Yang Y, Zhang X Y, Man X K, Zhang X H, Doi M, Yan L T. 2021. Enhanced heterogeneous diffusion of nanoparticles in semiflexible networks. ACS Nano, 15: 4608-4616. doi: 10.1021/acsnano.0c08877 Xu Z Y, Dai X B, Bu X Y, Yang Y, Zhang X Y, Man X K, Zhang X H, Doi M, Yan L T. 2021. Enhanced heterogeneous diffusion of nanoparticles in semiflexible networks. ACS Nano, 15: 4608-4616. doi: 10.1021/acsnano.0c08877
[285]	Xue C D, Huang Y R, Zheng X, Hu G Q. 2022. Hopping behavior mediates the anomalous confined diffusion of nanoparticles in porous hydrogels. J. Phys. Chem. Lett., 13: 10612-10620. Xue C D, Huang Y R, Zheng X, Hu G Q. 2022. Hopping behavior mediates the anomalous confined diffusion of nanoparticles in porous hydrogels. J. Phys. Chem. Lett., 13: 10612-10620.
[286]	Xue C D, Qu H C, Zheng G S, Qin K R, Zhao D W. 2022. Understanding the diffusive transport of nanoparticles in agarose hydrogels. Phys. Fluids, 34: 122001. doi: 10.1063/5.0127687 Xue C D, Qu H C, Zheng G S, Qin K R, Zhao D W. 2022. Understanding the diffusive transport of nanoparticles in agarose hydrogels. Phys. Fluids, 34: 122001. doi: 10.1063/5.0127687
[287]	Xue C D, Shi X H, Tian Y, Zheng X, Hu G Q. 2020. Diffusion of nanoparticles with activated hopping in crowded polymer solutions. Nano Lett., 20: 3895-3904. Xue C D, Shi X H, Tian Y, Zheng X, Hu G Q. 2020. Diffusion of nanoparticles with activated hopping in crowded polymer solutions. Nano Lett., 20: 3895-3904.
[288]	Xue C D, Yin Y F, Xu X Y, Tian K, Su J H, Hu G Q. 2025. Particle manipulation under X-force fields. Lab Chip, 25: 956-978. Xue C D, Yin Y F, Xu X Y, Tian K, Su J H, Hu G Q. 2025. Particle manipulation under X-force fields. Lab Chip, 25: 956-978.
[289]	Xue C D, Zheng X, Chen K K, Tian Y, Hu G Q. 2016. Probing non-gaussianity in confined diffusion of nanoparticles. J. Phys. Chem. Lett., 7: 514-519. doi: 10.1021/acs.jpclett.5b02624 Xue C D, Zheng X, Chen K K, Tian Y, Hu G Q. 2016. Probing non-gaussianity in confined diffusion of nanoparticles. J. Phys. Chem. Lett., 7: 514-519. doi: 10.1021/acs.jpclett.5b02624
[290]	Yang Y, Zeng W W, Huang P, Zeng X W, Mei L. 2021. Smart materials for drug delivery and cancer therapy. VIEW, 2: 20200042. Yang Y, Zeng W W, Huang P, Zeng X W, Mei L. 2021. Smart materials for drug delivery and cancer therapy. VIEW, 2: 20200042.
[291]	Yang Z L, Pei Z Y, Gao Z X, Luo M, Liu X C, Guo J, Jiang H Y, Lv M T, Yu Z L, Zhao S L, Guan J G. 2025. Bienzyme-powered nanorobots with ultrasensitive chemotaxis for precision cancer therapy. Natl. Sci. Rev., 13: nwaf580. doi: 10.1093/nsr/nwaf580 Yang Z L, Pei Z Y, Gao Z X, Luo M, Liu X C, Guo J, Jiang H Y, Lv M T, Yu Z L, Zhao S L, Guan J G. 2025. Bienzyme-powered nanorobots with ultrasensitive chemotaxis for precision cancer therapy. Natl. Sci. Rev., 13: nwaf580. doi: 10.1093/nsr/nwaf580
[292]	Yasuda K, Okamoto R, Komura S. 2017. Anomalous diffusion in viscoelastic media with active force dipoles. Phys. Rev. E, 95: 032417. Yasuda K, Okamoto R, Komura S. 2017. Anomalous diffusion in viscoelastic media with active force dipoles. Phys. Rev. E, 95: 032417.
[293]	Yeung P K. 2002. Lagrangian investigations of turbulence. Annu. Rev. Fluid Mech., 34: 115-142. Yeung P K. 2002. Lagrangian investigations of turbulence. Annu. Rev. Fluid Mech., 34: 115-142.
[294]	Yu C Q, Guan J, Chen K J, Bae S C, Granick S. 2013. Single-molecule observation of long jumps in polymer adsorption. ACS Nano, 7: 9735-9742. doi: 10.1021/nn4049039 Yu C Q, Guan J, Chen K J, Bae S C, Granick S. 2013. Single-molecule observation of long jumps in polymer adsorption. ACS Nano, 7: 9735-9742. doi: 10.1021/nn4049039
[295]	Yu L, Lei Y Z, Ma Y, Liu M, Zheng J J, Dan D, Gao P. 2021. A comprehensive review of fluorescence correlation spectroscopy. Front. Phys., 9: 644450. Yu L, Lei Y Z, Ma Y, Liu M, Zheng J J, Dan D, Gao P. 2021. A comprehensive review of fluorescence correlation spectroscopy. Front. Phys., 9: 644450.
[296]	Yu M R, Song W Y, Tian F L, Dai Z., Zhu Q L, Ahmad E, Guo S Y, Zhu C L, Zhong H J, Yuan Y C, Zhang T, Yi X, Shi X H, Gan Y, Gao H J. 2019. Temperature- and rigidity-mediated rapid transport of lipid nanovesicles in hydrogels. Proc. Natl. Acad. Sci. U. S. A., 116: 5362-5369. doi: 10.1073/pnas.1818924116 Yu M R, Song W Y, Tian F L, Dai Z., Zhu Q L, Ahmad E, Guo S Y, Zhu C L, Zhong H J, Yuan Y C, Zhang T, Yi X, Shi X H, Gan Y, Gao H J. 2019. Temperature- and rigidity-mediated rapid transport of lipid nanovesicles in hydrogels. Proc. Natl. Acad. Sci. U. S. A., 116: 5362-5369. doi: 10.1073/pnas.1818924116
[297]	Yu M R, Wang J L, Yang Y W, Zhu C L, Su Q, Guo S Y, Sun J S, Gan Y, Shi X H, Gao H J. 2016. Rotation-facilitated rapid transport of nanorods in mucosal tissues. Nano Lett., 16: 7176-7182. Yu M R, Wang J L, Yang Y W, Zhu C L, Su Q, Guo S Y, Sun J S, Gan Y, Shi X H, Gao H J. 2016. Rotation-facilitated rapid transport of nanorods in mucosal tissues. Nano Lett., 16: 7176-7182.
[298]	Yu M R, Xu L, Tian F L, Su Q, Zheng N, Yang Y W, Wang J L, Wang A H, Zhu C L, Guo S Y, Zhang X X, Gan Y, Shi X H, Gao H J. 2018. Rapid transport of deformation-tuned nanoparticles across biological hydrogels and cellular barriers. Nat. Commun., 9: 2607. Yu M R, Xu L, Tian F L, Su Q, Zheng N, Yang Y W, Wang J L, Wang A H, Zhu C L, Guo S Y, Zhang X X, Gan Y, Shi X H, Gao H J. 2018. Rapid transport of deformation-tuned nanoparticles across biological hydrogels and cellular barriers. Nat. Commun., 9: 2607.
[299]	Yücel H. 2023. A simulation study on colloid diffusion under time-varying optical potentials. J. Appl. Phys., 134: 013101. Yücel H. 2023. A simulation study on colloid diffusion under time-varying optical potentials. J. Appl. Phys., 134: 013101.
[300]	Zaburdaev V, Denisov S, Klafter J. 2015. Lévy walks. Rev. Mod. Phys., 87: 483-530. Zaburdaev V, Denisov S, Klafter J. 2015. Lévy walks. Rev. Mod. Phys., 87: 483-530.
[301]	Zhang B, Snezhko A. 2025. Shape-anisotropy inverses the behavior of emergent vortices in active chiral fluids. Commun. Phys., 8: 243. Zhang B, Snezhko A. 2025. Shape-anisotropy inverses the behavior of emergent vortices in active chiral fluids. Commun. Phys., 8: 243.
[302]	Zhang C, Liu R, Ding Z C, Lu P, Tian W M, Zhao Y. He J Y, Hou S G, 2025. Review of machine learning for single-particle tracking: methods, challenges, and biophysical insights. Chem. & Biomed. Imaging. Zhang C, Liu R, Ding Z C, Lu P, Tian W M, Zhao Y. He J Y, Hou S G, 2025. Review of machine learning for single-particle tracking: methods, challenges, and biophysical insights. Chem. & Biomed. Imaging.
[303]	Zhang J, Yang L J, Wang H X, Wang J L, Dong R Y. 2025. Cross-sectional effects on nanorod diffusion in Polymer melts. Macromolecules, 58: 4959-4970. Zhang J, Yang L J, Wang H X, Wang J L, Dong R Y. 2025. Cross-sectional effects on nanorod diffusion in Polymer melts. Macromolecules, 58: 4959-4970.
[304]	Zhang Y Y, Ge F, Lin X J, Xue J F, Song Y X, Xie H, He Y. 2023. Extract latent features of single-particle trajectories with historical experience learning. Biophys. J., 122: 4451-4466. doi: 10.1016/J.BPJ.2023.10.023 Zhang Y Y, Ge F, Lin X J, Xue J F, Song Y X, Xie H, He Y. 2023. Extract latent features of single-particle trajectories with historical experience learning. Biophys. J., 122: 4451-4466. doi: 10.1016/J.BPJ.2023.10.023
[305]	Zhang Y Y, Zhu J L, Xie H, He Y, 2025. Physics-informed deep learning for stochastic particle dynamics estimation. Proc. Natl. Acad. Sci. U. S. A. , 122: e2418643122. Zhang Y Y, Zhu J L, Xie H, He Y, 2025. Physics-informed deep learning for stochastic particle dynamics estimation. Proc. Natl. Acad. Sci. U. S. A. , 122: e2418643122.
[306]	Zhang Y, Dudko O K. 2016. First-passage processes in the genome. Annu. Rev. Biophys., 45: 117-134. doi: 10.1146/annurev-biophys-062215-010925 Zhang Y, Dudko O K. 2016. First-passage processes in the genome. Annu. Rev. Biophys., 45: 117-134. doi: 10.1146/annurev-biophys-062215-010925
[307]	Zheng X, Ten Hagen B, Kaiser A, Wu M L, Cui H H, Silber Li Z, Lowen H. 2013. Non-gaussian statistics for the motion of self-propelled janus particles: experiment versus theory. Phys. Rev. E, 88: 032304. doi: 10.1103/PhysRevE.88.032304 Zheng X, Ten Hagen B, Kaiser A, Wu M L, Cui H H, Silber Li Z, Lowen H. 2013. Non-gaussian statistics for the motion of self-propelled janus particles: experiment versus theory. Phys. Rev. E, 88: 032304. doi: 10.1103/PhysRevE.88.032304
[308]	Zhou H X, Rivas G, Minton A P. 2008. Macromolecular crowding and confinement: biochemical, biophysical, and potential physiological consequences. Annu. Rev. Biophys., 37: 375-397. Zhou H X, Rivas G, Minton A P. 2008. Macromolecular crowding and confinement: biochemical, biophysical, and potential physiological consequences. Annu. Rev. Biophys., 37: 375-397.
[309]	Zhou H, Chen S B. 2009. Brownian dynamics simulation of tracer diffusion in a cross-linked network. Phys. Rev. E, 79: 021801. Zhou H, Chen S B. 2009. Brownian dynamics simulation of tracer diffusion in a cross-linked network. Phys. Rev. E, 79: 021801.
[310]	Zuo W L, Wu, Y L. 2020. Dynamic motility selection drives population segregation in a bacterial swarm. Proc. Natl. Acad. Sci. U. S. A., 117: 4693-4700. Zuo W L, Wu, Y L. 2020. Dynamic motility selection drives population segregation in a bacterial swarm. Proc. Natl. Acad. Sci. U. S. A., 117: 4693-4700.
[311]	Zwanzig R. 1973. Nonlinear generalized langevin equations. J. Stat. Phys., 9: 215-220. Zwanzig R. 1973. Nonlinear generalized langevin equations. J. Stat. Phys., 9: 215-220.