Speed Limits on Pattern Formation in Dynamic Materials

该基金将资助研究，使材料的未来工程，形成功能模式响应外部触发，如光或热，应用于化学和光学传感器和微电子，从而促进科学的进步，促进国家繁荣。生命系统中的细胞物质可以迅速适应周围环境，相应地组织其结构模式。下一代人造材料的工程表现出这样的行为需要新的理论方法来澄清设计决策和功能模式形成的动态之间的关系。该项目将通过创造分析图案形成速率的新方法来解决这一需求，特别强调这种速率的上限，这将为未来在预定时间表上形成图案的材料的创造提供信息。这种智能材料将有利于能源、生物医学、化学和医疗保健行业的应用。在线开放科学计算笔记本将有助于让学生和其他研究人员广泛接触到模式形成的科学。与当地麦克奈尔学者项目的联系将有助于扩大目前代表性不足群体的学生参与STEM。本研究的目的是对与非平衡模式形成的瞬态动力学相关的速度限制的表征做出根本性的贡献。它将通过关注反应扩散系统中的模式形成来实现这一结果，这是一种动力机制，以前被用来制造微结构，实现新的传感器模式，并产生工作。理论框架将依赖于一个新的密度矩阵公式，受到经典统计力学和量子力学类比的启发。分析结果将使用数值模拟进行验证，从而允许对与瞬态模式形成相关的设计空间进行广泛的探索。目标理论将能够系统地区分确定性动力学和随机动力学的贡献，并将为可能使用控制来调节对瞬态波动的动态响应提供信息。该项目将为复杂动态系统行为的硅内设计奠定基础，在相空间和信息的几何形状之间产生计算上可处理的联系，并为系统对外部刺激的响应设定界限，这可以作为材料功能驱动的设计原则。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.