Critical Mechanical Structures: Topology and Entropy

该奖项支持软材料的理论研究、推广和教育，以及使用新概念设计新的机械超材料。机械稳定性的概念可以追溯到1864年麦克斯韦（j.c. Maxwell）的研究，它支配着软物质物理学中许多引人入胜的现象，从颗粒物质的干扰到新材料的自组装和生物组织的非线性弹性。同时，这一理念也指导着新型机械超材料的设计，这些超材料可以实现前所未有的功能。机械超材料通过其结构而不是其组成来获得新的机械性能。PI将研究机械不稳定性和软材料变形之间的相互作用，这种材料消耗很少的能量，称为软盘模式。结构可以被识别为在整体上是刚性的，但具有容易变形的软边缘，其基本特性是剥离软边缘会导致新材料也具有软边缘。利用最近发展的与拓扑学相关的概念，可以识别具有不同力学性能的材料相，拓扑学是数学的一个分支，涉及在变形下保存的物体的特性。PI将研究这些材料相，它们对缺陷和热驱动振动的鲁棒性，以及当材料接近机械不稳定性时，软变形如何在不同材料相之间转换材料。PI将利用从这些“拓扑保护”的机械相和它们之间的转换的研究中获得的理解来设计新的机械超材料。PI还将研究当这些新设备足够小，热波动是重要的，以及通过自组装生产这些结构时会发生什么。该项目不仅旨在对接近机械不稳定的结构的物理学有一个基本的了解，而且为具有坚固性能和功能的新一代机械材料的设计提供指导。此外，该项目还包括提高公众对软物质物理学及其对我们日常生活的贡献的认识的外展活动，以及通过在当地学校的外展和女物理学生的小组讨论扩大妇女和其他少数民族对物理学的参与的教育活动。该奖项支持软材料的理论研究、推广和教育，以及使用新概念设计新的机械超材料。软物质物理学中许多引人入胜的现象的核心是一组软盘模式，这是一种消耗很少能量的变形模式，是机械不稳定的信号。例子包括堵塞颗粒物质的屈服和生物组织的非线性弹性。与此同时，近年来对机械超材料的研究激增，这些材料是通过其结构而不是其成分获得新的机械性能，如负泊松比、负压缩率、负热膨胀、声子带隙等。有趣的是，在许多情况下，实现这些机械超材料新特性的关键，也是软盘模式的集合，这些软盘模式通常被称为机构。这个项目的目标是研究接近机械不稳定性和表现出软盘模式的结构的拓扑和熵。两个主要的重点是研究：(1)机械系统中的拓扑跃迁和可变换拓扑机械超材料的设计原则；(2)软盘模式的熵效应，这将用于理解机械超材料的自组装以及小尺度上具有抗波动机制的机器和机器人的设计原则。本项目将使用的方法包括解析理论和数值模拟。该项目的智力价值源于(1)关键机械结构的不寻常力学和声学特性的一般分类，(2)机械系统中新型拓扑跃迁的表征，这些跃迁与物质的量子拓扑状态的跃迁有着有趣的相似之处。(3)热波动对软盘模式的影响表征，软盘模式与拓扑具有有趣的相互作用，并指导鲁棒机制的选择；(4)新型开放结构的自组装设计和预测。该奖项还支持提高公众对软物质物理学及其对我们日常生活的贡献的宣传活动，以及通过在当地学校的宣传和女物理学学生的小组讨论来扩大妇女和其他少数民族对物理学的参与的教育活动。

NONTECHNICAL SUMMARYThis award supports theoretical research, outreach, and education on soft materials and designing new mechanical metamaterials using new concepts. The concept of mechanical stability, which dates back to the research of J. C. Maxwell in 1864, governs many fascinating phenomena in soft matter physics, from jamming of granular matter to self-assembly of novel materials and nonlinear elasticity of biological tissue. At the same time, this concept also guides the design of new mechanical metamaterials that can perform unprecedented functions. Mechanical metamaterials display novel mechanical properties acquired through their structure instead of their composition.The PI will investigate the interplay between mechanical instability and the deformations of a soft material that cost very little energy, called floppy modes. Structures can be identified that are rigid in the bulk but have soft edges that are easily deformed with a fundamental property that peeling away the soft edges leads to a new material that also has soft edges. Using recently developed concepts related to topology, the branch of mathematics concerned with the properties of objects that are preserved under deformations, material phases with different mechanical properties can be identified. The PI will study these material phases, how robust they are against imperfections and thermally driven vibrations, and how soft deformations can transform a material between different material phases when a material is close to a mechanical instability.The PI will use the understanding gained from the study of these "topologically protected" mechanical phases and the transformations among them to design new mechanical metamaterials. The PI will also study what will happen when these novel devices are made small enough that thermal fluctuations are important, as well as producing these structures via self-assembly.This project not only aims at a fundamental understanding of the physics of structures near mechanical instabilities, but also provides guidance to the design of new generation mechanical materials that have robust properties and functions. Moreover, the project includes outreach activities which increase the awareness of the general public on soft matter physics and its contributions to our daily life, as well as educational activities that broaden participation of women and other minorities in physics through outreach in local schools and group discussions among female physics students. TECHNICAL SUMMARYThis award supports theoretical research, outreach, and education on soft materials and designing new mechanical metamaterials using new concepts. Central to many fascinating phenomena in soft matter physics are a collection of floppy modes, which are modes of deformations that cost little energy and signals mechanical instability. Examples include the yielding of jammed granular matter and the nonlinear elasticity of biological tissue. In the meantime, recently there has been an explosion of investigations on mechanical metamaterials, which are materials that gain their novel mechanical properties, such as negative Poisson's ratio, negative compressibility, negative thermal expansion, phononic band-gap, via their structure instead of their composition. Interestingly, in many cases the key to realize the novel properties of these mechanical metamaterials, is also a collection of floppy modes, which are often called mechanisms.The goal of this project is to investigate the topology and entropy of structures that are close to mechanical instabilities and exhibit floppy modes. The two main thrusts are to investigate: (1) Topological transitions in mechanical systems and design principles of transformable topological mechanical metamaterials, (2) Entropic effects on floppy modes, which will be used to understand self-assembly of mechanical metamaterials as well as design principles of machines and robots at small scales with mechanisms robust against fluctuations. The methods that will be used in this project include analytic theory and numerical simulations.The intellectual merit of this project stems from (1) the general classification of the unusual mechanical and acoustic properties of critical mechanical structures, (2) the characterization of novel topological transitions in mechanical systems, which share intriguing similarities with transitions in quantum topological states of matter, (3) the characterization of thermal fluctuation effects on floppy modes that exhibit interesting interplay with topology and guides the selection of robust mechanisms, (4) the designs and predictions on the self-assembly of novel open structures.This award also supports outreach activities which increase the awareness of the general public on soft matter physics and its contributions to our daily life, as well as educational activities that broaden participation of women and other minorities in physics through outreach in local schools and group discussions among female physics students.