Rui: Active Noise in the Dynamics of Self-Propelled Particles – Stochastic Modeling and Experiments

原子的发现在19世纪初世纪是一个令人难以置信的科学成就和数学的发展的时间产生了不可或缺的现代技术必不可少的理解行为的噪音和随机过程。这些技术在气候学、天文学、经济学等广泛领域产生了基础性成果。如今，在有源噪声系统领域中，研究能够自我推进但受到噪声（随机性）影响的物体，如细胞或自主机器人，可能还有另一个重要的转折点，在那里，科学和数学的影响可以无数地造福于现代生活。该项目旨在通过开发个体代理的精确模型来发现和开发用于理解这些噪声主动系统的基本数学框架，即，一个细胞或单个机器人，并测试模型与实验测量。个体的运动是一个基本的构建块，对于解释存在于例如生物体、机器人探索或动态适应工程材料中的群体或群集行为至关重要。科学上，该项目将推进我们对有源噪声的基本理解，并为科学和工程应用的开发奠定基础。这项研究将在跨学科的环境中进行，学生将在新兴的有源噪声科学领域接受培训。有源噪声存在于广泛的系统中，它通常表现为一种非平衡力，不断引起复杂的动力学。近年来，由于主动噪声在活性物质和随机热力学的交叉学科领域中的重要性，人们对它的兴趣迅速增长。该项目将开发一个数学框架来模拟自推进粒子中的主动噪声及其与物理定律的联系。消耗能量驱动持续运动的主动自推进粒子是许多复杂动力学系统的模型构建块。研究有源噪声如何驱动动力学有望彻底改变我们对非平衡系统和相关数学技术的理解，就像我们对热噪声的数学理解彻底改变了热力学和材料科学一样。更具体地说，自推进粒子根据定义是不平衡的，因此经历非热活性波动。它们是研究粒子非平衡涨落的理想模型系统。本计画将发展欠阻尼自推进粒子的数学架构。它将通过以下步骤建立理解主动噪声的基本步骤：（1）建立具有完整惯性动力学的自推进粒子的随机模型;（2）开发模拟物理系统的主动噪声的真实模型;（3）通过随机热力学将主动噪声与物理学中的关系联系起来。广义朗之万方法将用于建模，实验将在微观和宏观尺度的自推进粒子在限制势。主动噪声存在于各种各样的系统中，包括信息系统、随机同步、流体湍流、活性物质、活生物体等。研究有源噪声如何揭示系统的潜在动力学，有可能对许多领域产生影响。该奖项反映了NSF的法定使命，并通过利用基金会的知识价值和更广泛的影响审查进行评估，被认为值得支持的搜索.

The discovery of the atom in the early 19th century was an incredible scientific achievement and the mathematical developments of the time yielded indispensable modern techniques essential for understanding the behavior of noisy and random processes. These techniques have produced fundamental results in a wide range of fields, such as climatology, astronomy, economics, and many more. Today, in the field of active noisy systems — e.g., the study of objects that propel themselves but are subjected to noise (randomness), such as cells or autonomous robots — there is potentially another important juncture, where both the scientific and mathematical implications can innumerably benefit modern life. This project aims to discover and develop the fundamental mathematical framework for understanding these noisy active systems by developing accurate models of the individual agents, i.e., of a cell or single robot, and testing the models with experimental measurements. Movement of the individuals is a fundamental building block that’s vital to explicating the group or flocking behaviors present in, for example, living organisms, robotic explorations, or dynamically-adapting engineered materials. Scientifically, this project will advance our fundamental understanding of active noise and set the stage for developing applications in science and engineering. This research will take place in an interdisciplinary environment and students will be trained in the emerging scientific field of active noise.Active noise exists in a wide range of systems, where it is often manifested as a non-equilibrium force that consistently induces complex dynamics. Recently, interest in active noise has grown rapidly because of its fundamental importance in the interdisciplinary fields of active matter and stochastic thermodynamics. This project will develop a mathematical framework to model active noise in self-propelled particles and its connection to physical law. Active self-propelled particles that consume energy to drive persistent motion are a model building block of many complex dynamical systems. Investigating how active noise drives dynamics holds promise to revolutionize our understanding of non-equilibrium systems and the associated mathematical techniques, much like our mathematical understanding of thermal noise revolutionized thermodynamics and material science. More specifically, self-propelled particles are by definition out-of-equilibrium and thus experience non-thermal active fluctuations. They serve as an ideal model system to study the non-equilibrium fluctuations of particles. This project will develop the mathematical framework for underdamped self-propelled particles. It will establish the foundational steps for understanding active noise by: (1) Building a stochastic model of self-propelled particles with the full inertial dynamics; (2) Developing a true model of active noise that mimics physical systems; and (3) Connecting active noise to relations in physics via stochastic thermodynamics. The generalized Langevin approach will be used for modeling, and experiments will done on both micro- and macro-scale self-propelled particles in confining potentials. Active noise is present in a wide variety of systems, including information systems, stochastic synchronization, fluid turbulence, active matter, living organisms, etc. Thus, studying how active noise can reveal the underlying dynamics of a system has potential to impact many fields.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.