Speed Limits on Pattern Formation in Dynamic Materials

这笔赠款将资助研究，使未来的材料工程，形成功能模式，以响应外部触发器，如光或热，应用于化学和光学传感器和微电子学，从而促进科学的进步和推进国家的繁荣。生命系统中的细胞材料可以迅速适应周围环境，相应地组织其结构模式。设计下一代人造材料以展示这种行为需要新的理论方法来阐明设计决策与功能图案形成动态之间的关系。该项目将通过创建分析图案形成速率的新方法来满足这一需求，特别强调这种速率的上限，这将为未来创建在预定时间表上形成图案的材料提供信息。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使学生和其他研究人员广泛接触模式形成的科学。推广到当地的麦克奈尔学者计划将有助于扩大参与STEM的学生从目前代表性不足的groups.This研究的目的是作出根本性的贡献与非平衡模式形成的瞬态动力学的速度限制的表征。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，这是一种动力学机制，以前曾被用来制造微结构，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，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进行验证，允许广泛的探索与瞬态图案形成相关的设计空间。目标理论将使确定性和随机动力学的贡献之间的系统分离，并将通知可能使用的控制来调节瞬态波动的动态响应。该项目将为复杂动态系统行为的计算机设计奠定基础，在相空间和信息的几何形状之间产生计算上易于处理的联系，并对系统对外部刺激的响应进行限制，这些外部刺激可以作为材料功能驱动的设计原则。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的学术价值和更广泛的影响评审标准。

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.