Path-dependency and emergent computing under vectorial driving
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866929751801724928 |
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| author | Meulblok, Colin M. Singh, Amitesh Labousse, Matthieu van Hecke, Martin |
| author_facet | Meulblok, Colin M. Singh, Amitesh Labousse, Matthieu van Hecke, Martin |
| contents | The sequential response of frustrated materials - ranging from crumpled sheets and amorphous media to metamaterials - reveals their memory effects and emergent computational potential. Despite their spatial extension, most studies rely on a single global stimulus, such as compression, effectively reducing the problem to scalar driving. Here, we introduce vectorial driving by applying multiple spatially localized stimuli to explore path-dependent, sequential responses. We uncover a wealth of phenomena absent in scalar driving, including non-Abelian responses, mixed-mode behavior, and chiral loop transients. We find that such path dependencies arise from elementary motifs linked to fold singularities, which connect triplets of states - ancestor, descendant, and sibling; and develop a general framework using pt-graphs to describe responses under any vectorial driving protocol. Leveraging binarized vectorial driving, we establish a natural connection to computation, showing that a single sample can encode multiple sequential Boolean circuits, which are selectable by driving strength and reprogrammable via additional inputs. Finally, we introduce graph-based motifs to manage the complexity of high-dimensional driving. Our work paves the way for strategies to explore, harness, and understand complex materials and memory, while advancing embodied intelligence and in-materia computing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07764 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Path-dependency and emergent computing under vectorial driving Meulblok, Colin M. Singh, Amitesh Labousse, Matthieu van Hecke, Martin Soft Condensed Matter The sequential response of frustrated materials - ranging from crumpled sheets and amorphous media to metamaterials - reveals their memory effects and emergent computational potential. Despite their spatial extension, most studies rely on a single global stimulus, such as compression, effectively reducing the problem to scalar driving. Here, we introduce vectorial driving by applying multiple spatially localized stimuli to explore path-dependent, sequential responses. We uncover a wealth of phenomena absent in scalar driving, including non-Abelian responses, mixed-mode behavior, and chiral loop transients. We find that such path dependencies arise from elementary motifs linked to fold singularities, which connect triplets of states - ancestor, descendant, and sibling; and develop a general framework using pt-graphs to describe responses under any vectorial driving protocol. Leveraging binarized vectorial driving, we establish a natural connection to computation, showing that a single sample can encode multiple sequential Boolean circuits, which are selectable by driving strength and reprogrammable via additional inputs. Finally, we introduce graph-based motifs to manage the complexity of high-dimensional driving. Our work paves the way for strategies to explore, harness, and understand complex materials and memory, while advancing embodied intelligence and in-materia computing. |
| title | Path-dependency and emergent computing under vectorial driving |
| topic | Soft Condensed Matter |
| url | https://arxiv.org/abs/2503.07764 |