Anomalous stochastic search

异常随机搜索

• 批准号: 2609335
• 金额: --
• 依托单位: Queen Mary University of London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2609335
• 关键词: Anomalous; stochastic; search

Background: Biological dynamics are characterised by activity in the sense that energy is taken up from the environment and converted into motion [1]. Examples of self-propelled motion range from human movement, to foraging marine predators, to crawling biological cells. Active dynamics are very different from passive Brownian motion, where a tracer particle is driven by collisions with the surrounding fluids particles. Biological processes furthermore often exhibit anomalous dynamics characterised by long-term diffusion that is, again, very different from Brownian motion [2]. This reflects the spatio-temporal complexity of biological systems. Mathematically both active and anomalous dynamics are modeled in terms of advanced (persistent, non-Markovian, non-Gaussian) stochastic processes [1,2]. This project will cross-link these two very recent, new fields of research for understanding the search of targets like, e.g., food sources in a foraging process [3].Project description: The warm-up will be to learn about Lévy walks, a famous fundamental class of anomalous stochastic processes [4]. Their diffusive properties should be understood analytically and explored numerically in simple search scenarios, formulated mathematically as first passage and first arrival problems. While much is known about these dynamics in one dimension, higher dimensional settings are at the forefront of research. This knowledge should be applied to understand new experimental data by G.Volpe (London) and V.Trianni (Rome) on biological and robotic Lévy walkers. The impact of biological activity and interactions between single particles on search efficiency should be explored by developing and analysing new stochastic models. References[1] C.Bechinger, R.Di Leonardo, H.Lowen, C.Reichhardt G.Volpe, G.Volpe, Rev.Mod.Phys. 88, 045006 (2016)[2] R.Klages, G.Radons, I.M.Sokolov (Eds.), Anomalous Transport: Foundations and Applications (Wiley-VCH, Berlin, 2008)[3] R.Klages, Search for food of birds, fish and insects, book chapter in: A.Bunde, J.Caro, J.Kaerger, G.Vogl (Eds.), Diffusive Spreading in Nature, Technology and Society. (Springer, Berlin, 2017)[4] V. Zaburdaev, S. Denisov, J. Klafter, Rev.Mod.Phys. 87, 483 (2015)

背景：生物动力学的特征是从环境中吸收能量并转化为运动的活动[1]。自我推进运动的例子从人类运动，到觅食的海洋捕食者，到爬行的生物细胞。主动动力学与被动布朗运动非常不同，被动布朗运动中示踪粒子是通过与周围流体粒子的碰撞来驱动的。此外，生物过程经常表现出以长期扩散为特征的异常动力学，这与布朗运动非常不同。这反映了生物系统的时空复杂性。在数学上，主动和异常动态都是根据高级（持续，非马尔可夫，非高斯）随机过程建模的[1，2]。该项目将交叉链接这两个非常新的研究领域，以了解目标的搜索，例如，[3].项目描述：热身将是学习Lévy Walks，一个著名的基本类的反常随机过程[4].它们的扩散特性应该在简单的搜索场景中进行分析和数值探索，在数学上表示为第一次通过和第一次到达问题。虽然在一维中对这些动力学有很多了解，但更高维度的设置处于研究的前沿。这些知识应该应用于理解G.Volpe（伦敦）和V.Trianni（罗马）关于生物和机器人Lévy步行者的新实验数据。应通过开发和分析新的随机模型来探索生物活动和单个粒子之间的相互作用对搜索效率的影响。参考文献[1] C.Bechinger，R.Di列奥纳多，H.Lowen，C.Reichhardt G.Volpe，G.Volpe，Rev.Mod.Phys. 88，045006（2016）[2] R.Klages，G.Radons，I.M.Sokolov（Eds.），异常运输：基础和应用（Wiley-VCH，柏林，2008年）[3] R.Klages，搜索鸟类，鱼类和昆虫的食物，书籍章节：A.Bunde，J.Caro，J.Kaerger，G.Vogl（编辑），在自然、技术和社会中的扩散传播。（Springer，柏林，2017）[4] V. Zaburdaev，S. Denisov，J. Klafter，Rev.Mod.Phys. 87，483（2015）