Speed Limits on Pattern Formation in Dynamic Materials

动态材料中图案形成的速度限制

• 批准号: 2124510
• 负责人: Jason Green
• 金额: $ 37.44万
• 依托单位: University of Massachusetts Boston
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-09-01 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2124510&HistoricalAwards=false
• 关键词: Speed; Limits; Pattern; Formation; Dynamic

This grant will fund research that enables future engineering of materials that form functional patterns in response to external triggers such as light or heat, with application to chemical and optical sensors and microelectronics, thereby promoting the progress of science and advancing the national prosperity. Cellular materials in living systems can quickly adapt to their surroundings, organizing their structural patterns accordingly. Engineering the next generation of human-made materials to exhibit such behavior requires new theoretical methods to clarify the relationship between design decisions and the dynamics of functional pattern formation. This project will address this need by creating new methods for the analysis of the rates of pattern formation, with particular emphasis on upper bounds on such rates that would inform the future creation of materials that form patterns on predetermined time schedules. Such smart materials will benefit applications across the energy, biomedical, chemical, and healthcare industries. Online, open-science computational notebooks will help make the science of pattern formation widely accessible to students and other researchers. Outreach to a local McNair Scholars Program will help broaden participation in STEM of students from currently underrepresented groups.This research aims to make fundamental contributions to the characterization of speed limits associated with the transient dynamics of nonequilibrium pattern formation. It will accomplish this outcome by focusing on pattern formation in reaction-diffusion systems, a dynamical mechanism that has previously been leveraged to fabricate microstructures, enable new sensor modalities, and generate work. The theoretical framework will rely on a new density matrix formulation, inspired by classical statistical mechanics and quantum-mechanical analogies. Analytical results will be validated using numerical simulations that permit a broad exploration of the design space associated with transient pattern formation. The target theory will enable a systematic separation between the contributions of deterministic and stochastic dynamics, and will inform the possible use of control to regulate the dynamic response to transient fluctuations. The project will lay the groundwork for in-silico design of the behaviors of complex dynamic systems, produce computationally tractable links between the geometries of phase space and information, and place bounds on the response of systems to external stimuli that can serve as a design principle for the actuation of material functionality.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.

这笔赠款将用于研究，使未来能够对光或热等外部触发形成功能模式的材料进行工程设计，并应用于化学和光学传感器和微电子，从而促进科学进步和国家繁荣。生命系统中的细胞材料可以迅速适应环境，相应地组织它们的结构模式。设计下一代人造材料来展示这种行为需要新的理论方法来澄清设计决策和功能模式形成动力学之间的关系。本项目将通过创造分析图案形成速度的新方法来满足这一需要，特别强调这种速度的上限，这将为未来按预定时间表形成图案的材料的创造提供信息。这种智能材料将使能源、生物医药、化工和医疗保健行业的应用受益。在线，开放科学的计算笔记本将有助于让学生和其他研究人员更广泛地接触到模式形成的科学。与当地麦克奈尔学者项目的接触将有助于扩大来自目前代表性不足群体的学生对STEM的参与。本研究旨在为描述与非平衡模式形成的瞬时动态相关的速度限制做出基础性贡献。它将通过专注于反应扩散系统中的图案形成来实现这一结果，反应扩散系统是一种以前被用来制造微结构、实现新的传感器模式和产生功的动力学机制。理论框架将依赖于一种新的密度矩阵公式，灵感来自经典统计力学和量子力学类比。分析结果将使用数值模拟来验证，数值模拟允许对与瞬变图案形成相关的设计空间进行广泛的探索。目标理论将使确定性动力学和随机动力学的贡献得以系统地分离，并将为可能使用控制来调节对瞬时波动的动态反应提供信息。该项目将为复杂动态系统行为的计算机设计奠定基础，在相空间的几何形状和信息之间产生易于计算的联系，并为系统对外部刺激的响应设定界限，作为物质功能驱动的设计原则。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Speed limits on deterministic chaos and dissipation

• DOI: 10.1103/physrevresearch.5.l012016
• 发表时间: 2023-02
• 期刊: Physical Review Research
• 影响因子: 4.2
• 作者: Swetamber Das;Jason R. Green

Density matrix formulation of dynamical systems

动力系统的密度矩阵公式

• DOI: 10.1103/physreve.106.054135
• 发表时间: 2022
• 期刊: Physical Review E
• 影响因子: 2.4
• 作者: Das, Swetamber;Green, Jason R.
• 通讯作者: Green, Jason R.