多稳态材料的矢量驱动：奇点、路径转换图和非一般路径
Vectorial driving of multistable materials: singularities, pt-graphs, and non-generic paths
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中文总结 AI 辅助
研究多稳态材料矢量驱动，结合实验与模型，探讨高阶奇点对路径转换图及响应的影响，讨论非一般驱动路径作用，展示t-图与pt-图关系，建立基于奇点的路径相关响应方法，为相关材料设计提供基础。
中文摘要 AI 辅助
描述和预测多稳态材料对外部驱动的响应对于记忆形成、可编程超材料、软机器人技术和材料内计算至关重要。标量驱动由过渡图（t-图）捕获，而矢量驱动产生与路径相关的响应，这需要最近引入的路径过渡图（pt-图）。在这两种情况下，转变都由能量景观中的奇点控制：标量驱动对应鞍结分岔，矢量驱动高阶奇点变得重要。通过将链状超材料实验与最小弹簧模型相结合，我们研究高阶奇点如何塑造pt-图以及由此产生的与路径相关的响应。我们还讨论了通过高阶奇点的非一般驱动路径的作用，其响应由自发对称破缺控制。最后，我们展示了t-图如何作为pt-图的一维极限出现，在基于图的通用框架内统一标量和矢量驱动。这些结果建立了一种基于奇点的方法来处理与路径相关的响应，并为设计具有可编程顺序功能的多稳态材料提供了基础，用于智能传感、软机器人技术和材料内计算。
英文摘要
Describing and predicting the response of multistable materials to external driving is central to memory formation, programmable metamaterials, soft robotics, and in-materia computing. While scalar driving is captured by transition graphs (t-graphs), vectorial driving produces path-dependent responses that require the recently introduced path-transition graphs (pt-graphs). In both cases, transitions are governed by singularities in the energy landscape: for scalar driving these correspond to saddle-node bifurcations, but for vectorial driving, higher-order singularities become important. Combining experiments on chain-like metamaterials with a minimal spring model, we investigate how higher-order singularities shape pt-graphs and the resulting path-dependent responses. We moreover discuss the role of non-generic driving paths through higher-order singularities, where the response is governed by spontaneous symmetry breaking. Finally, we demonstrate how t-graphs emerge as the one-dimensional limit of pt-graphs, unifying scalar and vectorial driving within a common graph-based framework. These results establish a singularity-based approach to path-dependent responses and provide a foundation for designing multistable materials with programmable sequential functionality for smart sensing, soft robotics, and in-materia computation.
